Exponential and Logarithmic Functions.docx

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LASALLIAN NxGEN BLENDED LEARNING MODULE

Teacher:

Teacher: Sofia T. PaclarinSofia T. Paclarin Mark

Mark Josep Josep L. L. Men!o"aMen!o"a Al#er$

Al#er$ Morris Morris Pa%ila%anPa%ila%an

Gra!e"Year Le#e$:

Gra!e"Year Le#e$: J&niorsJ&niors S%&'ec(:S%&'ec(: Ma$e'a$icsMa$e'a$ics

Ter):

Ter): (( U*+( T,+c:U*+( T,+c: Exponen$ial an!Exponen$ial an! Lo%ari$'ic )&c$ions Lo%ari$'ic )&c$ions

T+)e ra)e:

T+)e ra)e: ** !a+s** !a+s

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The $ear*er !e),*(ra(e %*!er(a*!+*/ , (he e The $ear*er !e),*(ra(e %*!er(a*!+*/ , (he e c,*ce( , e3,*e*(+a$ a*! $,/ar+(h)+c e4%a(+,*. c,*ce( , e3,*e*(+a$ a*! $,/ar+(h)+c e4%a(+,*.

The $ear*er + a&$e (,

The $ear*er + a&$e (, +*#e(+/a(e (h,r,%/h$+*#e(+/a(e (h,r,%/h$

)a(he)a(+ca$ re$a(+,*h+ +* #ar+,% +(%a(+,* a*! )a(he)a(+ca$ re$a(+,*h+ +* #ar+,% +(%a(+,* a*! ,r)%$a(e rea$-$+e r,&$e) +*#,$#+*/ e3,*e*(+a$ a*! ,r)%$a(e rea$-$+e r,&$e) +*#,$#+*/ e3,*e*(+a$ a*! $,/ar+(h)+c e4%a(+,* a*! ,$#e (hee %+*/ a

$,/ar+(h)+c e4%a(+,* a*! ,$#e (hee %+*/ a #ar+e(#ar+e( , (ra(e/+e +(h %(),( a

, (ra(e/+e +(h %(),( a cc%rac.cc%rac.

LASALLIAN GUIDING PRIN,IPLES

Chec a$+ca&$e LGP Chec a$+ca&$e LGP

✔

LGP 1: Cha$$e*/e $ear*er (, rea$+e (he+r %$$ ,(e*(+a$.LGP 1: Cha$$e*/e $ear*er (, rea$+e (he+r %$$ ,(e*(+a$.

✔

LGP 2: 7r+*/ Chr+(+a* erec(+#e (, &ear ,* h%)a* LGP 2: 7r+*/ Chr+(+a* erec(+#e (, &ear ,* h%)a* %*!er(a*!+*/8 +$$ a*! #a$%e , (he %*!er(a*!+*/8 +$$ a*! #a$%e , (he $ear*er.$ear*er. LGP 9:Are !*a)+c a*! e*c,%ra/e !+ere*(+a(+,*8 !+#er+( a*! *er/ a),*/( $ear*er (ha( are LGP 9:Are !*a)+c a*! e*c,%ra/e !+ere*(+a(+,*8 !+#er+( a*! *er/ a),*/( $ear*er (ha( are r+e*!$

r+e*!$8 car+*/ 8 car+*/ a*! a*! reec(%$.reec(%$.

✔

LGP : E*%re (ha( $ear*er (ra*$a(e *,$e!/e +*(, ,)e(h+*/ %e%$ +* LGP : E*%re (ha( $ear*er (ra*$a(e *,$e!/e +*(, ,)e(h+*/ %e%$ +* ac(%a$ rac(+ce ,r (heac(%a$ rac(+ce ,r (he &e((er)e*( , ,c+e(.

&e((er)e*( , ,c+e(.

✔

LGP 5: Preare $ear*er (, LGP 5: Preare $ear*er (, ar(+c+a(e re,*+&$ +* (he ar(+c+a(e re,*+&$ +* (he ,r$! , ,r8 a)+$8 c,))%*+(,r$! , ,r8 a)+$8 c,))%*+(8 *a(+,*8 a*!8 *a(+,*8 a*! ch%rch.

ch%rch.

STA

GE -

ESTA

BLIS/ED

DESIRED RESU

LTS

TRANS)ER GOALS

Students will independently use their learning to Students will independently use their learning to

h, (he+r ,* %*!er(a*!+*/ ,* (he &a+c c,*ce( , e3,*e*(+a$ a*! $,/ar+(h)+c e4%a(+,* +* a r,!%c( ,r h, (he+r ,* %*!er(a*!+*/ ,* (he &a+c c,*ce( , e3,*e*(+a$ a*! $,/ar+(h)+c e4%a(+,* +* a r,!%c( ,r er

er,r,r)a*)a*ce ce hehere re (he(he  ++$$ $$ rr+(e +(e a a rere,r( ,r( ,r ,r rr,,,,a$ a$ ,r (he ,r (he &e&e( ( +*#+*#e(e()e*)e*( ( ,(,(+,* ,r +,* ,r (he(he+r +r ),*),*ee8 8 +*+* c,*+!era(+,* , (he ,$$,+*/ ac(,r: 1; +*(ere( ra(e8 2; c,),%*!+*/ er+,! <4%ar(er$8 ),*(h$8 ,r !a+$; a*!8 c,*+!era(+,* , (he ,$$,+*/ ac(,r: 1; +*(ere( ra(e8 2; c,),%*!+*/ er+,! <4%ar(er$8 ),*(h$8 ,r !a+$; a*!8 9; $e*/(h , c,*(rac( <1

9; $e*/(h , c,*(rac( <1 ear8 2 ear8 e(c.ear8 2 ear8 e(c.; (ha( (he !+ere*( &a* ,er.; (ha( (he !+ere*( &a* ,er.

ENDURING UNDERSTANDING

Students will understand that ... Students will understand that ...

E3,*e*(+a$ a*! $,/ar+(h)+c %*c(+,* ha#e

E3,*e*(+a$ a*! $,/ar+(h)+c %*c(+,* ha#e c,rre,*!+*/ r,er(+e.c,rre,*!+*/ r,er(+e.

L,/ar+(h) ca* &e %e! (, ,$#e e3,*e*(+a$ e4%a(+,*= a*! c,*#ere$8 e3,*e*( ca* &e %e! (, ,$#e L,/ar+(h) ca* &e %e! (, ,$#e e3,*e*(+a$ e4%a(+,*= a*! c,*#ere$8 e3,*e*( ca* &e %e! (, ,$#e $,/ar+(h)+c e4%a(+,*.

$,/ar+(h)+c e4%a(+,*. E3

E3,*e,*e*(+*(+a$ a$ %*%*c(+c(+,* ,* are are ++!e$!e$  %e%e! ! +* +* rearea$ $ ,r,r$!8 $!8 %c%ch h a a +(+(%a(%a(+,*+,*  ),!),!e$ee$e! ! & & e3e3,*e,*e*(+*(+a$ a$ /r/r,(,(hh <arec+a(+,*; ,r !eca <!erec+a(+,*;8 +* +*a*ce a*! &a*+*/ <+*#e()e*(8 cre!+( car!8 $,a* a*!

<arec+a(+,*; ,r !eca <!erec+a(+,*;8 +* +*a*ce a*! &a*+*/ <+*#e()e*(8 cre!+( car!8 $,a* a*! (he+r %e , (he+r %e , c,),%*! +*(ere(;8 (, (he (%! , &+,$,/+ca$ ,%$a(+,* a*! (he+r ra(e , /r,(h <ha$-$+e;8 a*! e#e* +* c,),%*! +*(ere(;8 (, (he (%! , &+,$,/+ca$ ,%$a(+,* a*! (he+r ra(e , /r,(h <ha$-$+e;8 a*! e#e* +* archae,$,/ a*! a$e,*(,$,/ a*! car&,* !a(+*/.

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L,/ar+(h) ,cc%r +* (he h+ca$ a*! &+,$,/+ca$ c+e*ce8 +* e!%ca(+,*8 +* (a(+(+c8 a*! ec,*,)+c8 (, *a)e a e. L,/ar+(h) are e3(re)e$ %e%$ ,r c,)%(a(+,*a$ %r,e a*! ca* a$$, ,*e (, +*! (he #a$%e , a* %**,* e3,*e*(8 re#+,%$ ,*$ a((a+*a&$e (hr,%/h /%e-,r.

ESSENTIAL 0UESTIONS

Students will find the answer to the question…

H, are e3,*e*(+a$ a*! $,/ar+(h)+c %*c(+,* re$a(e!>

H, ca* e3,*e*(+a$ a*! $,/ar+(h)+c %*c(+,* &e % e! (, +)$+ ,$%(+,* (, rea$-$+e r,&$e)>

A,0UISITION GOALS

,o'pe$encies 1DepE! ,o!e2

3NO4LEDGE PRO,ESS UNDERSTANDING

A. E3,*e*(+a$ %*c(+,*: De+*+(+,* = Grah= Pr,er(+e= La , E3,*e*(= E3,*e*(+a$ E4%a(+,*

• De+*e #er&a$$ a*! +* r+(+*/

a* e3,*e*(+a$ %*c(+,*.

• I$$%(ra(e +* r+(+*/ (he /rah

, e3,*e*(+a$ %*c(+,*.

• I!e*(+ #er&a$$ a*! +* r+(+*/

(he r,er(+e , a* e3,*e*(+a$ %*c(+,*.

• I!e*(+ #er&a$$ a*! +* r+(+*/

(he $a , e3,*e*(.

• S+)$+ +* r+(+*/ e3re+,*

%+*/ $a , e3,*e*(. B. L,/ar+(h)+c %*c(+,*:

De+*+(+,* = Grah= Pr,er(+e= La , L,/ar+(h)= C,*#er+,*= L,/ar+(h)+c E4%a(+,*= C,)),* a*! Na(%ra$ L,/ar+(h)=

L,/ar+(h) (, O(her 7ae

• De+*e #er&a$$ a*! +* r+(+*/

a $,/ar+(h)+c %*c(+,*.

• I$$%(ra(e +* r+(+*/ (he /rah

, $,/ar+(h)+c %*c(+,*.

• I!e*(+ #er&a$$ a*! +* r+(+*/

(he r,er(+e , a $,/ar+(h)+c %*c(+,*.

• C,*#er( +* r+(+*/ e3,*e*(+a$

a*! $,/ar+(h)+c e4%a(+,*.

• I!e*(+ +* r+(+*/ a*! #er&a$$

(he r,er(+e ,r $a , $,/ar+(h).

• S+)$+ +* r+(+*/ e3re+,*

%+*/ r,er(+e ,r $a , $,/ar+(h).

B. E3,*e*(+a$ %*c(+,*: De+*+(+,* = Grah= Pr,er(+e= La , E3,*e*(= E3,*e*(+a$ E4%a(+,* • S,$#e +* r+(+*/ e3,*e*(+a$ e4%a(+,* %+*/ $a , e3,*e*(. B. L,/ar+(h)+c %*c(+,*:

De+*+(+,* = Grah= Pr,er(+e= La , L,/ar+(h)= C,*#er+,*= L,/ar+(h)+c E4%a(+,*= C,)),* a*! Na(%ra$ L,/ar+(h)=

L,/ar+(h) (, O(her 7ae

• S,$#e +* r+(+*/ $,/ar+(h)+c e4%a(+,*. ,. A$+ca(+,*: S,$#e ?,r! Pr,&$e) • Crea(e +* r+(+*/ rea$-$+e +(%a(+,* +*#,$#+*/ e3,*e*(+a$ a*! $,/ar+(h)+c e4%a(+,*.

• S,$#e +* r+(+*/ rea$-$+e

+(%a(+,*" r,&$e) +*#,$#+*/ e3,*e*(+a$ a*! $,/ar+(h)+c e4%a(+,*.

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STAGE * DETERMINING 5ALID E5IDEN,E 6 ASSESSMENT

PRODUCT OR PERORMANCE SHO?ING E@IDENCE O UNDERSTANDING  TRANSER

S(%!e*( +$$ r+(e a re,r( ,r r,,a$ ,r (he &e( +*#e()e*( ,(+,* ,r (he+r ),*e8 +* c,*+!era(+,* , (he ,$$,+*/ ac(,r: 1; +*(ere( ra(e8 2; c,),%*!+*/ er+,! <4%ar(er$8 ),*(h$8 ,r !a+$; a*!8 9; $e*/(h , c,*(rac( <1 ear8 2 ear8 e(c.; (ha( (he !+ere*( &a* ,er.

GRASPS NARRATI@E O TRANSER TASB

In$ro!&c$ion

S,)e,*e ha &ee* !+$+/e*($ a#+*/ ),*e ,r (he a( e ear a*! ha acc%)%$a(e! Ph1008 000 +* cah. The /,a$ ha &ee* (, a#e % e*,%/h ),*e (, &% a %e! car. He !e(er)+*e (ha( +( ,%$! &e &e((er (, +*#e( (he ),*e +* a &a* a*! c,$$ec( +*(ere( %*(+$ he + rea! (, )ae h+ &+/ %rchae. A(er ea+*/ +(h ,%8 a &a* reree*(a(+#e8 he + /+#e* e#era$ !+ere*( a#+*/ ,(+,*. Y,% +$$ %e ,%r a&+$+( (, ,r +(h e3,*e*(+a$ a*! $,/ar+(h)+c %*c(+,* (, !e(er)+*e (he &e( a#+*/ $a* ,% ca* ,er.

Task

I* (h+ r,'ec( ,% +$$ $a (he r,$e , a &a* reree*(a(+#e (, he$ ,)e,*e ee+*/ (, +*#e( ),*e +* a a#+*/ acc,%*( ,r a cer(++ca(e , !e,+( <CD;. ?he* c,*+!er+*/ !+ere*( +*#e()e*( ,(+,* (here are e#era$ ac(,r (, c,*+!er: 1; +*(ere( ra(e 2; c,),%*!+*/ er+,! <4%ar(er$8 ),*(h$8 ,r !a+$; a*! 9; $e*/(h , c,*(rac( <1 ear8 2 ear8 e(c.;. ?,r+*/ (,/e(her +(h ,%r /r,%8 ,% +$$ a*a$e !a(a a*! )ae ca$c%$a(+,* (, !e(er)+*e (he &e( +*#e()e*( ,(+,* ,r ,%r c$+e*( ),*e.

Ins$r&c$ions

S,$#e each r,&$e) +* ,r!er a*! a#e ,%r ,r a$,*/ (he a8 a ,% +$$ crea(e a re,r( ,r r,,a$ a( (he c,*c$%+,* , (he r,'ec(. Y,%r ,%(%( +$$ &e ree*(e! ,r ar,#a$ (, (he &a* c$+e*(. The r,,a$ +$$ &e ar,#e! &ae! ,* (he ,$$,+*/ cr+(er+a: C,*(e*(8 a*! Pree*(a(+,*"C,))%*+ca(+,*

Reference $$p66777.'on$ere+ins$i$&$e.or%6co&rses6De8elop'en$alMa$6PD*9:RESOUR,E6p!&-;.p!f

SCAOLD OR TRANSER

LE@EL 1 D+rec(e! Pr,)( LE@EL 2 Oe* Pr,)( LE@EL 9 G%+!e! Tra*er LE@EL  I*!ee*!e*( Tra*er U+*/ De),8 (%!e*(

+$$ &e ae! (, /rah (he e3,*e*(+a$ a*!

$,/ar+(h)+c %*c(+,*. The +$$ a$, &e ae! (,

+!e*(+ (he+r r,er(+e %+*/ G%+!e %e(+,*. The +$$ a$, &e h,* e3a)$e (, ee h, La , E3,*e*( a*!

Pr,er(+e , L,/ar+(h) ca* &e %e! a*! a$+e! +* ,$#+*/ e3,*e*(+a$ a*! $,/ar+(h)+c e4%a(+,*. ?,rhee( +$$ &e r,#+!e! (, &e acc,)$+he! e+(her +*!+#+!%a$$8 +* a+r8 ,r +* /r,% ,r (he) (, rac(+ce (he )a(he)a(+ca$ +$$.

The (%!e*( +$$ &e /r,%e! +*(, . Each /r,% +$$ &e ae! (, +!e*(+ a( $ea( 5 rea$-$+e +(%a(+,* here

e3,*e*(+a$ a*!

$,/ar+(h)+c %*c(+,* are a$+e! ,r %e!. The +$$ &e re4%+re! (, reare a ree*(a(+,* %+*/ a* )e!+%) <P,erP,+*(8 c,$$a/e8 e(c.;.

Rea$-$+e r,&$e) a&,%( c,),%*! +*(ere( a*! ha$-$+e +$$ &e ree*(e! (, (he (%!e*(. S(%!e*( +$$ &e ae! (, a*a$e a*! ,$#e (he) a (he (eacher /%+!e (he).

The (%!e*( <+* /r,% , (hree; +$$ &e ae! (, a*er Activity Sheet #10 a&,%( ,$#+*/ rea$-$+e +(%a(+,* %+*/

e3,*e*(+a$ a*! $,/ar+(h)+c %*c(+,*. There +$$ a$, &e har+*/ , ,$%(+,* a*! +*a$ a*er.

S(%!e*( +$$

+*!ee*!e*($ %e (he+r $ear*+*/ (, h, (he+r ,* %*!er(a*!+*/ ,* (he &a+c c,*ce( , e3,*e*(+a$ a*! $,/ar+(h)+c e4%a(+,* +* a r,!%c( ,r

er,r)a*ce here (he +$$ r+(e a re,r( ,r r,,a$ ,r (he &e( +*#e()e*( ,(+,* ,r (he+r ),*e8 +* c,*+!era(+,* , (he ,$$,+*/ ac(,r: 1; +*(ere( ra(e8 2; c,),%*!+*/ er+,! <4%ar(er$8 ),*(h$8 ,r !a+$; a*!8 9; $e*/(h , c,*(rac( <1 ear8 2 ear8 e(c.; (ha( (he !+ere*( &a* ,er.

ASSESSMENT TOOLS <U+( Ae)e( Ma;

(4)

PERORMANCE Pre- Ae)e*("D+a/*, (+c  O*$+*e Pre-(e( <G,,/$e ,r);  Teacher-)a!e ?,rhee(  Teacher-)a!e ?,rhee( ,r)a(+#e  Me*(a$ Dr+$$  Teacher-)a!e ?,rhee(  Grah+c Or/a*+er  Teacher-)a!e ?,rhee(  Teacher-)a!e ,rhee(

S%))a(+#e  O*$+*e P,((e( <G,,/$e ,r);  Ae)e*(

 Ae)e*(  Ae)e*( A r+((e* re,r( ,r r,,a$ ,r (he &e( +*#e()e*( ,(+,* ,r (he+r ),*e8 +* c,*+!era(+,* , (he ,$$,+*/ ac(,r: 1; +*(ere( ra(e8 2; c,),%*!+*/ er+,! <4%ar(er$8 ),*(h$8 ,r !a+$; a*!8 9; $e*/(h , c,*(rac( <1 ear8 2 ear8 e(c.; (ha( (he !+ere*( &a* ,er.

Se$-Ae)e*(  Per,r)a*ce

Ta Re$ec(+,*

RELATED ACETS O UNDERSTANDING

• A$ ,r)%$a (, ,$#e ,r! r,&$e).

• E3$a+* h, (, %e a*! )a*+%$a(e ,r)%$a (, ,$#e #ar+,% rea$-$+e r,&$e) ,* +*#e()e*(8 ,%$a(+,*

/r,(h ,r !eca8 ha$-$+e8 ra!+,ac(+#e )a(er+a$8 a*! a(),her+c re%re.

• I*(erre( re%$( !er+#e! a( +* %+*/ ,r )a*+%$a(+*/ ,r)%$a.

BLENDED A,TI5ITIES6TOOLS

EN@IRONMENT

ATTRI7UTES

ACE-TO-ACE

E-LEARNING

ACTI@E  Class Discussion and Evaluation  Problem Solving

 Oral Recitation

 Me*(a$ C,)%(a(+,* a*! Re#+e , c,*ce( %+*/ ah,,(.+(

 Ue , De), (, /rah %*c(+,*  Ue , <Ma(hT,,*Me!+a; (, *, h, (, c,*#er( e3,*e*(+a$ ,r) (, $,/ar+(h)+c ,r) a*! #+ce-#era.  h((:"".,%(%&e.c,)"a(ch>

#A1BT+7T re#+e , (he La , E3,*e*(

 h((:"".,%(%&e.c,)"a(ch> #BFP+PY3(a,8 h, h, (he /rah , e3,*e*(+a$ %*c(+,* a*! $,/ar+(h)+c %*c(+,* are re$a(e!

COLLA7ORATI@E _ _{Pa+r-,r a*! Gr,% ,r ac(+#+(+e} _ _{Ue , G,,/$e C$ar,,) a*!}

Sch,,$,/ a Lear*+*/ Ma*a/e)e*( S(e) here (%!e*( a*!

(eacher ca* c,$$a&,ra(e8 a*! e3cha*/e +!ea.

(5)

$ea( 5 rea$-$+e +(%a(+,* here e3,*e*(+a$ a*! $,/ar+(h)+c %*c(+,* are a$+e! ,r %e!.

c,$$a/e8 e(c.; (, reare a ree*(a(+,*.

AUTHENTIC  ?r+(+*/ , a re,r( ,r r,,a$ ,r (he &e( +*#e()e*( ,(+,* ,r (he+r ),*e8 +* c,*+!era(+,* , (he ,$$,+*/

ac(,r: 1; +*(ere( ra(e8 2;

c,),%*!+*/ er+,! <4%ar(er$8 ),*(h$8 ,r !a+$; a*!8 9; $e*/(h , c,*(rac( <1 ear8 2 ear8 e(c.; (ha( (he !+ere*( &a* ,er.

 Ue , a* )e!+%) <P,erP,+*(8 c,$$a/e8 e(c.; (, reare a r+((e* re,r( ,r r,,a$ a*! <I),#+e8 e(c; (, !,c%)e*( (he +*(er#+e a*! reearch !,*e.

GOAL-DIRECTED  Ue , Grah+c Or/a*+er

 Ue , Per,r)a*ce Ta Re$ec(+,*

STAGE ( LEARNING PLAN )LO4

LESSON PROPER

INTRODUCTION

DA< -64EE3 - 1Da$e Jan&ar+ -=>**? *@-2

OBJE,TI5ES A( (he e*! , (he er+,!8 (he (%!e*( are e3ec(e! (,:

1. A*er (he 15-+(e) re (e( ,* (he &a+c c,*ce( a&,%( e3,*e*(8 e3,*e*(+a$ e4%a(+,*8 $,/ar+(h) a*! +( r,er(+e8 a*! $,/ar+(h)+c e4%a(+,*.

2. I!e*(+ (he ee*(+a$ 4%e(+,* ,r (he $ear*+*/ ),!%$e. 9. I!e*(+ (he er,r)a*ce (a ,r (he $ear*+*/ ),!%$e.

A. Da+$ C$ar,,) R,%(+*e: Oe*+*/ raer8 Gree(+*/8 Chec+*/ , a((e*!a*ce8 C$ar,,) %ee

7. D+c%+,*

A( (he (ar( , (he %*+(8 (he (eacher +$$ h,, (he (%!e*( & a+*/ (ha( (he e*! /,a$ , (he %*+( + (ha( (%!e*( +$$ +*! (he a*er (, (he 4%e(+,*

H, are e3,*e*(+a$ a*! $,/ar+(h)+c %*c(+,* re$a(e!>

H, ca* e3,*e*(+a$ a*! $,/ar+(h)+c %*c(+,* &e %e! (, +)$+ ,$%(+,* (, rea$-$+e r,&$e)> The +$$ a$, &e +*,r)e! (ha( + (he +$$ %*!er(a*! (he &a+c c,*ce( , e3,*e*(+a$ a*! $,/ar+(h)+c %*c(+,*8 (he* (he +$$ h, (he+r %*!er(a*!+*/ ,* (he+r ,* +* a r,!%c( ,r er,r)a*ce here (he +$$ r+(e a re,r( ,r r,,a$ ,r (he &e( +*#e()e*( ,(+,* ,r (he+r ),*e8 +* c,*+!era(+,* , (he ,$$,+*/ ac(,r: 1; +*(ere( ra(e8 2; c,),%*!+*/ er+,! <4%ar(er$8 ),*(h$8 ,r !a+$; a*!8 9; $e*/(h , c,*(rac( <1 ear8 2 ear8 e(c.; (ha( (he !+ere*( &a* ,er.

II. INTERACTION

DA< *64EE3 - 1Da$e Jan&ar+ -=>**? *@-2

OBJE,TI5ES A( (he e*! , (he er+,!8 (he (%!e*( are e3ec(e! (,: 1. De+*e a* e3,*e*(+a$ %*c(+,*.

2. I$$%(ra(e (he /rah , e3,*e*(+a$ %*c(+,*. 9. I!e*(+ (he r,er(+e , a* e3,*e*(+a$ %*c(+,*.

(6)

A. C$ar,,) R,%(+*e: Oe*+*/ raer8 Gree(+*/8 Chec+*/ , a((e*!a*ce8 C$ar,,) %ee 7. D+c%+,*

1. U+*/ ah,,(.+(8 (he (%!e*( +$$ &e h,* e#era$ %*c(+,* a*! (he +$$ &e ae! (, +!e*(+ + (he /+#e* %*c(+,* + $+*ear8 4%a!ra(+c ,r e3,*e*(+a$. A(er h+ch8 (he (%!e*( +$$ &e ae! (, !+ere*(+a(e ,*e %*c(+,* r,) (he ,(her.   23 1.   3  9 2.   32_{ 93  2} 9.   3 1 .   93  1 5.   523-9 G&i!e 0&es$ions

a. ?h+ch , (he /+#e* are $+*ear %*c(+,*> %a!ra(+c %*c(+,*> E3,*e*(+a$ %*c(+,*> &. H, + $+*ear %*c(+,* !+ere*( r,) a 4%a!ra(+c %*c(+,*>

c. ?ha( + a* e3,*e*(+a$ %*c(+,*> H, + +( !+ere*( r,) $+*ear a*! 4%a!ra(+c %*c(+,*> The (eacher +$$ $+(e* (, (he (%!e*( #ar+*/ a*er.

The ,$$,+*/ e c,*ce( +$$ &e r,cee!:

a. A $+*ear %*c(+,* ca* &e r+((e* a y = ax + b8 here a, b ∈ ℜ _{; a}≠ _0 .

&. A %*c(+,* (ha( ca* &e r+((e* a y = a2 _{x + bx + c 8 here a, b and c}_{∈ ℜ}_{; a}_≠_0 . c. A* e3,*e*(+a$ %*c(+,* ca* &e r+((e* a y = a x

8 here a  0 &%( a≠ _!.

!. I* (he /+#e* %*c(+,*8 2 a*! 5 are $+*ear= 9 + 4%a!ra(+c= a*! 18  a*! 6 are e3,*e*(+a$ %*c(+,*. 2. The (%!e*( +$$ &e ree*(e! +(h (h+ +(%a(+,*:

S&ppose a c&l$&re of #ac$eria is p&$ in a Pe$ri !is an! i$ !o&#les e8er+ 'in&$e. /o7 'an+ #ac$eria 7ill $ere #e af$er 9 'in&$es

The (%!e*( <+* a+r; +$$ &e ae! (, !, (he ,$$,+*/:

1. C,)$e(e (he (a&$e ,r (he a),%*( , (+)e a*! (he *%)&er , &ac(er+a r,!%ce!. A*a$e (he (a&$e. 2. I!e*(+ h+ch + (he +*!ee*!e*( #ar+a&$e a*! h+ch + (he !ee*!e*( #ar+a&$e.

9. ,r)%$a(e a* e4%a(+,* +* (, #ar+a&$e (ha( )a reree*( (he /+#e* +(%a(+,*.

. Decr+&e (he re$a(+,*h+ &e(ee* (he a),%*( , (+)e +(h (he *%)&er , &ac(er+a &e+*/ r,!%ce!. The h,%$! &e a&$e (, c,)e % +(h (he ,$$,+*/ a*er:

A),%*( , T+)e

<+* )+*%(e;

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The a),%*( , (+)e + (he +*!ee*!e*( #ar+a&$e h+$e (he *%)&er , &ac(er+a &e+*/ r,!%ce! + (he !ee*!e*( #ar+a&$e.

A %*c(+,*   23_{ca* reree*( (he /+#e* +(%a(+,*.}

Th+ e3a)$e + e3,*e*(+a$ +* *a(%re a*! + a+! (, &e a* increasing function or an exponential growth . 9. The (%!e*( <+* a+r; +$$ &e ae! (, !ra (he /rah , (he %*c(+,*   23

%+*/ De),.

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9. ?ha( + (he &eha#+,%r , (he /rah r,) $e( (, r+/h(> . D,e (he /rah a (hr,%/h (he *e/a(+#e -a3+> 5. ?ha( + (he 3-+*(erce(> Y-+*(er3ce(>

6. Grah (he %*c(+,*  

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The ,$$,+*/ e c,*ce( h,%$! &e !+c%e!:

PROPERTIES O) ECPONENTIAL )UN,TION 1. D,)a+*: a$$ rea$ *%)&er

Ra*/e: a$$ ,+(+#e *%)&er

2. 7eha#+,r he* a K 1: I*crea+*/ r,) $e( (, r+/h( 7eha#+,r he* 0  a  1: Decrea+*/ r,) $e( (, r+/h( 9. A)(,(e: A)(,(+c (, (he 3-a3+

. I*(erce(: 3  +*(erce(  *,*e   +*(erce(  1 ,r   <1"2;3

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. @ALUES INTEGRATION: The (%!e*( +$$ &e ae! + (he &e$+e#e +* (he a+*/8 THE MORE8 THE MERRIER. A(er h+ch8 (he +$$ &e ae! (, a(ch (h+ #+!e,8 h((:"".,%(%&e.c,)"a(ch>

#!$B@F+ . The ,r$! ,%$a(+,* + /r,+*/ e3,*e*(+a$$8 a Laa$$+a*8 h, ca* ,% c,*(r+&%(e +* ,%r ,* a (, he$ a!!re (h+ r,&$e)>

5. The (%!e*( +$$ &e /+#e* a (eacher-)a!e ,rhee(8 Activity Sheet 18 ,r (he+r a+/*)e*(.

DA< -64EE3 * 1Da$e Jan&ar+ *9>*=? *@-2

OBJE,TI5ES A( (he e*! , (he er+,!8 (he (%!e*( are e3ec(e! (,: 1. I!e*(+ (he $a , e3,*e*(.

2. S+)$+ e3re+,* %+*/ $a , e3,*e*(.

(8)

1. I* a+r8 (he (%!e*( +$$ &e ae! (, a*er Activity Sheet 2 8 here (he *ee! (, +)$+ e3re+,* +*#,$#+*/ $a , e3,*e*(. Th+ + (, ae + (%!e*( (+$$ re)e)&er $a , e3,*e*(. A(er 10 )+*%(e8 (%!e*( +$$ &e ae! (, !+c% (he+r a*er +(h a*,(her a+r.

2. The (%!e*( +$$ &e ae! (, a(ch a #+!e,8 h((:"".,%(%&e.c,)"a(ch>#A1BT+7T ? a&,%( La , E3,*e*(. The +$$ &e ae! (, c,%*(erchec (he+r ,r +(h (he /+#e* e3a)$e.

9. The c$a +$$ &e /%+!e! +* %))ar++*/ (he !+ere*( $a , e3,*e*(.

. The (%!e*( +$$ &e /+#e* a (eacher-)a!e ,rhee(8 Activity Sheet 38 ,r (he+r a+/*)e*(.

DA< *64EE3 * 1Da$e Jan&ar+ *9>*=? *@-2

OBJE,TI5ES A( (he e*! , (he er+,!8 (he (%!e*( are e3ec(e! (,: 1. De+*e e3,*e*(+a$ e4%a(+,*.

2. I!e*(+ The Pr,er( , E4%a$+( ,r E3,*e*(+a$ E4%a(+,*. 9. S,$#e e3,*e*(+a$ e4%a(+,* %+*/ $a , e3,*e*(.

1. The (%!e*( <+* /r,% , ; +$$ &e r,#+!e! +(h Activity Sheet 48 here (he +$$ ae! (, ,$#e (he /+#e* e3,*e*(+a$ e4%a(+,* & %+*/ (he ,$$,+*/ /+#e* +*,r)a(+,*:

(9)

Te Proper$+ of E&ali$+ for Exponen$ial E&a$ion

A* e3,*e*(+a$ e4%a(+,* +* ,*e #ar+a&$e + a* e4%a(+,* here (he e3,*e*( + (he #ar+a&$e. I* ,$#+*/ e3,*e*(+a$ e4%a(+,*8 (he Pr,er( , E4%a$+( ,r E3,*e*(+a$ E4%a(+,* + %e!. I( + (a(e! a

I a8 &8 a*! c are rea$ *%)&er a*! a  08 (he*8 a&_{ a}c_{+ a*! ,*$ + &  c.}

2. A(er (he a$$,((e! (+)e (he (%!e*( a*er +$$ &e chece!8 a+*/ (he) (, e3$a+* h, (he a$+e! (he /+#e* r,er( (, ,$#e (he /+#e* e3,*e*(+a$ e4%a(+,*.

9. @ALUES INTEGRATION: Ar+(,($e a+! (ha( The ,r( ,r) , +*e4%a$+( + (, )ae %*e4%a$ (h+*/ e4%a$. H, !,e (h+ a$ (, (he ree*( (+)e> A Laa$$+a*8 h, ,%$! ,% c,*(r+&%(e (, e4%a$+( a),*/ e#er,*e>

. A (eacher-)a!e ac(+#+( hee(8 Activity Sheet 5 8 +$$ &e /+#e* a a* a+/*)e*(.

DA< (64EE3 * 1Da$e Jan&ar+ *9>*=? *@-2

1. A*er (he 1-+(e) <99 ,+*(; %))a(+#e ae)e*( a&,%( e3,*e*(+a$ %*c(+,*8 +( /rah a*! r,er(+e= $a , e3,*e*(.

A. C$ar,,) R,%(+*e: Oe*+*/ raer8 Gree(+*/8 A((e*!a*ce chec+*/8 C$ar,,) %ee 7. The (%!e*( +$$ &e /+#e* a 10-15 )+*%(e re#+e &e,re (he (ae (he %))a(+#e ae)e*(.

DA< -64EE3 ( 1Da$e )e#r&ar+ ->9? *@-2

OBJE,TI5ES A( (he e*! , (he er+,!8 (he (%!e*( are e3ec(e! (,: 1. De+*e a $,/ar+(h)+c %*c(+,*.

2. I$$%(ra(e (he /rah , $,/ar+(h)+c %*c(+,*. 9. I!e*(+ (he r,er(+e , a $,/ar+(h)+c %*c(+,*. 4. C,*#er( e3,*e*(+a$ a*! $,/ar+(h)+c e4%a(+,*.

A. C$ar,,) R,%(+*e: Oe*+*/ raer8 Gree(+*/8 A((e*!a*ce chec+*/8 C$ar,,) %ee 7. D+c%+,*

1. The ,$$,+*/ c,*ce( h,%$! &e !+c%e!:

a. A %*c(+,* + a ec+a$ +*! , a re$a(+,* &e(ee* (, e(8 Q a*! Y8 %ch (ha( ,r e#er e$e)e*( +* e( Q (here + e3ac($ ,*e e$e)e*( a,c+a(e! +* e( Y.

&. The +*#ere , a %*c(+,* <!e*,(e! &  -1

; + a %*c(+,*" re$a(+,* h,e !,)a+* + (he ra*/e , (he /+#e* %*c(+,* a*! h,e ra*/e + (he !,)a+*. T, ,$#e ,r (he +*#ere , a %*c(+,*"re$a(+,*8 +*(ercha*/e (he #ar+a&$e 3 a*!  +* (he !e+*+*/ e4%a(+,*   <3;8 (he* ,$#e ,r  +* (er) , 3.

c. T, +*! (he +*#ere , (he e3,*e*(+a$ %*c(+,*8   a3

Exponen$ial )&nc$ion In8erse f&nc$ion

y = a x

x = ay

Y,% +$$ *,(+ce (ha( (he +*#ere , (he

e3,*e*(+a$ %*c(+,* h, (ha( y + (he

e3,*e*( (, h+ch (he &ae a + ra+e! +*

(10)

The +*#ere , (he e3,*e*(+a$ %*c(+,* a&,#e + ca$$e! logarith"ic function. The %*c(+,* + !e+*e! & (he e4%a(+,*

The e4%a(+,* , a $,/ar+(h)+c %*c(+,* + rea! a + is $e lo%ari$' of x $o $e #ase a . Tae *,(e (ha( +* (he *,(a(+,*8 a + (he &ae8 x + (he ,er a*! y + (he e3,*e*( (, h+ch a + ra+e! +* ,r!er (, ,&(a+* x.

2. The (%!e*( +$$ &e ae! (, a(ch a #+!e,8 https://www.youtube.com/watch?v=K_PiPfYxtao,h,+*/ h, (he /rah , e3,*e*(+a$ %*c(+,* a*! $,/ar+(h)+c %*c(+,* are re$a(e!. A(er a(ch+*/ (he #+!e, (he (%!e*( +$$ &e ae! (, hare (he +),r(a*( c,*ce( (he $ear*e!.

T, !ra (he /rah ,   $,/238 reca$$ (he /rah ,   23. $+ (he /rah ,   23a&,%( (he $+*e   38 h+ch + (he a3+ , ))e(r. Y,% h,%$! &e a&$e (, ,&er#e (ha( (he (, /rah c,*(a+* (he ,$$,+*/ +*(e/ra$

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a. The r,er(+e , (he +r( /rah +$$%(ra(e (he r,er(+e , $,/ar+(h)+c %*c(+,* +* (he ,r)   a3_{8 a K} 1. The !,)a+* + (he e( , a$$ ,+(+#e rea$ *%)&er a*! (he ra*/e are a$$ rea$ *%)&er.

2. The 3-+*(erce( + <1. 0; a*! +( a)(,(e + (he -a3+.

9. The %*c(+,* + ,+(+#e ,r a$$ 3 /rea(er (ha* 1 a*! *e/a(+#e ,r a$$ 3 $e (ha* 1. . The %*c(+,* + +*crea+*/.

&. The r,er(+e , (he ec,*! /rah +$$%(ra(e (he ,$$,+*/ r,er(+e , $,/ar+(h)+c %*c(+,* +* (he ,r)   a3_{8 0  a  1.}

1. The !,)a+* + (he e( , a$$ ,+(+#e rea$ *%)&er a*! (he ra*/e are a$$ rea$ *%)&er. 2. The 3-+*(erce( + <1. 0; a*! +( a)(,(e + (he -a3+

9. The %*c(+,* + *e/a(+#e ,r a$$ 3 /rea(er (ha* 1 a*! ,+(+#e ,r a$$ 3 $e (ha* 1. . The %*c(+,* + !ecrea+*/.

9. The (%!e*( +$$ &e h,* a* IPa! a$+ca(+,* <Ma(hT,,*Me!+a;8 h,+*/ h, (, c,*#er( e3,*e*(+a$ ,r) (, $,/ar+(h)+c ,r).

The (%!e*( +$$ &e re)+*!e! (ha( +( + ,(e* he$%$ (, *, h, (, c,*#er( a* e3,*e*(+a$ e4%a(+,* (, a $,/ar+(h)+c e4%a(+,* a*! #+ce #era. H,e#er8 (he ha#e (, *,(e (ha( (he !,)a+* , (he $,/ar+(h)+c %*c(+,* + re(r+c(e! (, #a$%e /rea(er (ha* er,8 (here,re8 e3,*e*(+a$ e4%a(+,* +(h a *e/a(+#e &ae ca**,( &e c,*#er(e! +*(, a $,/ar+(h)+c e4%a(+,*.

. The (%!e*( +$$ &e ae! (, a*er ,*e , (he ee*(+a$ 4%e(+,* & +$$+*/ ,%( (he /+#e* /rah+c ,r/a*+er. H, are e3,*e*(+a$ a*! $,/ar+(h)+c %*c(+,* re$a(e!>

(12)

5. The (%!e*( +$$ &e /+#e* a (eacher-)a!e ,rhee( a* a+/*)e*(8 Activity Sheet 6 .

DA< *64EE3 ( 1Da$e )e#r&ar+ ->9? *@-2

OBJE,TI5ES A( (he e*! , (he er+,!8 (he (%!e*( are e3ec(e! (,: -. I!e*(+ (he r,er(+e ,r $a , $,/ar+(h).

2. S+)$+ e3re+,* %+*/ r,er(+e ,r $a , $,/ar+(h).

-. The (%!e*( +$$ &e ree*(e! +(h (he ,$$,+*/ +*,r)a(+,*. A. Te Lo%ari$' of a Pro!&c$

Le( M  a3

a*! N  a .

7 La , E3,*e*( ,r Pr,!%c(8 MN  a3_a_{ a}3  _. 7 !e+*+(+,* , $,/ar+(h)+c %*c(+,*8 M  a3_{ $,/} aM  38 N  a  $,/aN  8 a*! MN  a3  _{ $,/} aMN  3  . 7 %&(+(%(+,*8 $,/aMN  $,/aM  $,/aN.

From the derivation, the logarithm of the product of to num!er" i" the "um of the logarithm" of the to factor"

B. Te Lo%ari$' of a 0&o$ien$

Ue (he /+#e* +* A a*! (he La , E3,*e*( ,r %,(+e*(8

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(13)

7 !e+*+(+,* , $,/ar+(h)+c %*c(+,*8 M  a3_{ $,/} aM  38 N  a_{ $,/} aN  8 a*!

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From the derivation, the logarithm of the $uotient of to num!er" i" the difference of the logarithm" of the dividend and the divi"or

,. Te Lo%ari$' of a Po7er Le( M  a3_.

7 (he La , E3,*e*( ,r a P,er8 M_{ <a}3_;_. 7 !e+*+(+,* , $,/ar+(h)+c %*c(+,*8 M  a3_{ $,/} aM  38 a*! M  <a3 ;  $,/aM  3. 7 %&(+(%(+,*8 $,/aM  $,/aM

From the derivation, the logarithm of the % th

poer of a num!er i" % time" the logarithm of the num!er

2. The (%!e*( +$$ &e /+#e* Activity Sheet & 8 here (he +$$ +)$+ e3re+,* %+*/ (he !+ere*( r,er(+e , $,/ar+(h).

9. The +$$ &e /+#e* Activity Sheet ' a (he+r a+/*)e*(.

DA< (64EE3 ( 1Da$e )e#r&ar+ ->9? *@-2

1. A*er (he 22-+(e) <92 ,+*(; %))a(+#e ae)e*( a&,%( $,/ar+(h)+c %*c(+,*8 +( /rah a*! r,er(+e= $a , $,/ar+(h).

C$ar,,) R,%(+*e: Oe*+*/ raer8 Gree(+*/8 A((e*!a*ce chec+*/8 C$ar,,) %ee The (%!e*( +$$ &e /+#e* a 10-15 )+*%(e re#+e &e,re (he (ae (he %))a(+#e ae)e*(.

DA< -64EE3 F 1Da$e )e#r&ar+ ;>-*? *@-2

OBJE,TI5ES A( (he e*! , (he er+,!8 (he (%!e*( are e3ec(e! (,: 1. De+*e $,/ar+(h)+c e4%a(+,*.

2. S,$#e $,/ar+(h)+c e4%a(+,*.

C$ar,,) R,%(+*e: Oe*+*/ raer8 Gree(+*/8 A((e*!a*ce chec+*/8 C$ar,,) %ee D+c%+,*

(14)

-. The (%!e*( +$$ &e ae! (, a*er #er&a$$ (he ,$$,+*/ 4%e(+,*:

a. ?ha( + $,/ar+(h)+c e4%a(+,*> H, !,e +( !+er r,) a* e3,*e*(+a$ e4%a(+,*> &. H, ca* e ,$#e a $,/ar+(h)+c e4%a(+,*>

The ,$$,+*/ e c,*ce( h,%$! &e !+c%e!:

a. E4%a(+,* (ha( c,*(a+* $,/ar+(h)+c e3re+,* are $,/ar+(h)+c e4%a(+,*.

&. T, ,$#e $,/ar+(h)+c e4%a(+,*8 +r( ,&(a+* a +*/$e $,/ar+(h)+c e3re+,* ,* ,*e +!e , (he e4%a(+,* a*! (he* r+(e a* e4%+#a$e*( e3,*e*(+a$ e4%a(+,*.

2. The ,$$,+*/ e3a)$e +$$ &e ree*(e! a*! !+c%e! +(h (he (%!e*(. Sol8e $e 'issin% $er's in $e follo7in% lo%ari$'ic e&a$ions. 1. $,/6 216  3

Tra*,r) $,/6216  3 +* e3,*e*(+a$ ,r)8 (he* ,$#e ,r 3. 63  216 63_{ 6}9 3  9 Chec: I 3  98 (he* 69  216. ∴$,/6 216  9 a*! 3  9. 2. x 2 3

₌

₈₁

3  96 3  2 Chec: I 3  28 (he* 22"9_{ <9}6_;2"9_{ 9}_{ J1} ∴ 3  2. 9. $,/ <53  ;  9 53    9 53    6 53  6   53  60 3 60"5 3  12 Chec: I 3  58 (he* $,/5<12;  V  $,/<60  ;  $,/ 6  9. ∴ 3  5 . $,/ <232 - 3  ;  $,/ <32 - 3  6;

S+*ce &,(h +!e , (he e4%a(+,* are +* &ae 108 (he* 232_{- 3    3}2_{- 3  6}

232

- 3    <32

- 3  6;  0 #ddition $roperty of %quality 32_₂₃_-₁₅_₀ _Si"plify

<3  5;<3 - 9;  0 &actoring 3  5  0 ,r 3 - 9  0

(15)

3  - 5 ,r 3  9 Chec: I 3  - 58 (he* $,/ <232_{- 3  ;  $,/ 2<-5;}2_{- <-5;  V}  $,/ 2<25;  95  V  $,/ <50  95  ;  $,/ 6 a*! $,/ <32_{- 3  6;  $,/ <-5;}2_{- <-5;  6V}  $,/ <25  5  6;  $,/ 6. He*ce8 3  - 5 + a ,$%(+,* I 3  98 (he* $,/ <232_{- 3  ;  $,/ 2<9;}2_{- <9;  V}  $,/ 2<;  21  V  $,/ <1J  21  ;  $,/ <-12;

He*ce8 3  9 + *,( a r,,( +*ce $,/ar+(h) + !e+*e! ,*$ ,r ,+(+#e *%)&er. ∴ 3  -5 + (he ,*$ ,$%(+,*.

N,(+ce (ha( (, ,$#e r,&$e) 1 (, 9 (he $,/ar+(h)+c e4%a(+,* ere +r( (ra*,r)e! +*(, e3,*e*(+a$ e4%a(+,*.

9. The (%!e*( +$$ &e /+#e* Activity Sheet # ( a a+/*)e*(. DA< * an! (64EE3 F 1Da$e )e#r&ar+ ;>-*? *@-2

1. I!e*(+ rea$-$+e +(%a(+,* %+*/ e3,*e*(+a$ a*! $,/ar+(h)+c %*c(+,*.

C$ar,,) R,%(+*e: Oe*+*/ raer8 Gree(+*/8 A((e*!a*ce chec+*/8 C$ar,,) %ee D+c%+,*

1. The (%!e*( +$$ &e /r,%e! +*(, . Each /r,% +$$ &e ae! (, +!e*(+ a( $ea( 5 rea$-$+e +(%a(+,* here e3,*e*(+a$ a*! $,/ar+(h)+c %*c(+,* are a$+e! ,r %e!. The +$$ &e re4%+re! (, reare a ree*(a(+,* %+*/ a* )e!+%) <P,erP,+*(8 c,$$a/e8 e(c.;. Th+ +$$ &e ree*(e! (, (he c$a (he ,$$,+*/ )ee(+*/.

(16)

DA< -64EE3 F 1Da$e )e#r&ar+ -9>-=? *@-2

OBJE,TI5ES A( (he e*! , (he er+,!8 (he (%!e*( are e3ec(e! (,: 1. S,$#e r,&$e) +*#,$#+*/ e3,*e*(+a$ a*! $,/ar+(h)+c e4%a(+,*.

1. Th+ r,&$e) +$$ &e ree*(e! (, (he (%!e*(:

Pr,&$e): E3a)+*e (he (, c,)),* +*#e()e*( che)e &e$,. ?h+ch che)e /+#e a h+/her +e$! +* a a* , 9 ear + I  Pr(>

A: P108000 !e,+(e! a( 1.5W +)$e +*(ere(

7: P108000 !e,+(e! a( 1.5W c,),%*!e! a**%a$$

A$$, (he (%!e*( (, e3cha*/e +!ea a*! ,+*+,* a*! %,r( (he+r a*er %+*/ )a(he)a(+ca$ c,)%(a(+,* $+e (h+ ,*e.

<ear - <ear * <ear (

Sche)e A 108150 108900 10850

Sche)e 7 108150 108902.25 10856.J

2. The (%!e*( +$$ &e +*,r)e! (ha( c,),%*! +*(ere( + a* e3a)$e , a* e3,*e*(+a$ %*c(+,*. Thecompoundinterestisgivenby:

A

=

P

(

1 +

r

)

t

here

P + (he r+*c+a$

A + (he a),%*( a(er ( ear r + (he +*(ere( ra(e

* + (he *%)&er , (+)e +*(ere( + c,),%*!e! +* a ear <*  2 + e)+-a**%a$$= *   + 4%ar(er$8 *  12 + ),*(h$.;

E3a)$e 1: S%,e Ph 8000 r+*c+a$ + +*#e(e! a( 6W +*(ere( a*! +e$! Ph 5959. ,r h, )a* ear a +( +*#e(e!>

?e %e (he ,r)%$a

_A

=

_P

(

₁

+

_r

)

t .

1 +

0.06 ¿

¿

5353

=

4000

¿

The* e ,$#e ,r (.

log 5353

=[

4000

(

1.06 )

t

]

log5353

=

log 4000

+

t

log1.06

log5353

−

log 4000

log 1.06

=

t

3.7286

−

3.6021

0.0253

≈ t

(17)

Te 'one+ 7as in8es$e! for approxi'a$el+ 9 +ears.

9. E3,*e*(+a$ %*c(+,* ca* a$, &e a$+e! +* !e(er)+*+*/ (he alf>life , a ra!+,ac(+#e %&(a*ce= +( + (he $e*/(h , (+)e ,r ,*e-ha$ , (he %&(a*ce (, !eca.

The ha$-$+e a),%*( A , a %&(a*ce re)a+*+*/ a(er (+)e ( + /+#e* & (he e3,*e*(+a$ e4%a(+,*

A

=

A 0

(

1

2

)

t n

here A0 + (he ,r+/+*a$ a),%*(8

* + (he ha$-$+e , a %&(a*ce.

E3a)$e 2. S%,e (ha( (he ha$-$+e , a cer(a+* ra!+,ac(+#e %&(a*ce +  !a. I*+(+a$$8 (here are 20 /ra) ree*( +* a c,*(a+*er.

Ue (he ha$-$+e ,r)%$a (, c,)%(e (he a),%*( , %&(a*ce $e( a(er 92 !a.

. The (%!e*( +$$ &e ae! (, a*er (he ,(her Ee*(+a$ %e(+,* %+*/ a* , (he (, /rah+c ,r/a*+er &e$,.

/o7 can exponen$ial an! lo%ari$'ic f&nc$ions #e &se! $o si'plif+ sol&$ions $o real>life pro#le's

DA< *>(64EE3 F 1Da$e )e#r&ar+ -9>-=? *@-2

OBJE,TI5ES A( (he e*! , (he er+,!8 (he (%!e*( are e3ec(e! (,: 1. S,$#e r,&$e) +*#,$#+*/ e3,*e*(+a$ a*! $,/ar+(h)+c e4%a(+,*.

1. The (%!e*( <+* /r,% , (hree; +$$ &e ae! (, a*er Activity Sheet #10 a&,%( ,$#+*/ rea$-$+e +(%a(+,* %+*/ e3,*e*(+a$ a*! $,/ar+(h)+c %*c(+,*.

(18)

DA< -64EE3 9 1Da$e )e#r&ar+ **>*? *@-2

OBJE,TI5ES

1. A*er (he F-+(e) <F,+*(; %))a(+#e ae)e*( a&,%( ,$#+*/ $,/ar+(h)+c e4%a(+,* a*! ,$#+*/ rea$-$+e +(%a(+,* +*#,$#+*/ e3,*e*(+a$ a*! $,/ar+(h)+c %*c(+,*.

A. C$ar,,) R,%(+*e: Oe*+*/ raer8 Gree(+*/8 A((e*!a*ce chec+*/8 C$ar,,) %ee 7 .The (%!e*( +$$ &e /+#e* a 10-15 )+*%(e re#+e &e,re (he (ae (he %))a(+#e ae)e*(.

DA< *64EE3 9 1Da$e )e#r&ar+ **>*? *@-2

OBJE,TI5ES

1. A*er (he 20-+(e) <20 ,+*(; ,((e( a&,%( e3,*e*(+a$ a*! $,/ar+(h)+c %*c(+,*. A. C$ar,,) R,%(+*e: Oe*+*/ raer8 Gree(+*/8 A((e*!a*ce chec+*/8 C$ar,,) %ee

7 .The (%!e*( +$$ &e /+#e* a 10-15 )+*%(e re#+e &e,re (he (ae (he ,((e(.

III. INTEGRATION

DA< (64EE3 F 1Da$e )e#r&ar+ **>*? *@-2

1. Groupings and Presentation of Proect Speci!cations

"#e students are given t#e mec#anics of t#e proect $#ic# t#e% need to accomplis# for t#e proect ma&ing da%s. "#e rubric $ill also be presented in class.

'. (rainstorming

"#e students brainstorm for t#e proect. "#e teac#er entertains )uestions raised b% t#e students

about t#e proect.

DA< ->(64EE3 9 1Da$e )e#r&ar+ *=>Marc F? *@-2

1. Pr,'ec( Ma+*/

The (%!e*( ,r ,* (he r,'ec(. The (eacher /%+!e (he (%!e*( h+$e ,r+*/ ,* (he r,'ec(.

DA< ->(64EE3  1Da$e Marc -F>-;? *@-2

1. Pr,'ec( Pree*(a(+,*

The (%!e*( ree*( (he+r ,%(%(. The (eacher a*! (%!e*( a 4%e(+,* re$a(e! (, (he ree*(a(+,*.

(19)

 h((:"".,%(%&e.c,)"a(ch>#A1BT+7T re#+e , (he La , E3,*e*(

 h((:"".,%(%&e.c,)"a(ch>#BFP+PY3(a, 8 h, h, (he /rah , e3,*e*(+a$ %*c(+,* a*! $,/ar+(h)+c %*c(+,* are re$a(e!

 h((:"".,%(%&e.c,)"a(ch>#!$B@F+8 h, h, (he ,r$! ,%$a(+,* + /r,+*/ e3,*e*(+a$$ &%( (he ear(h a*! +( re,%rce !, *,(

h((:"".),*(ere+*(+(%(e.,r/"c,%re"De#e$,)e*(a$Ma(h"PD25FRESOURCE"!%1J.! ,%rce ,r er,r)a*ce (a

 A$/e&ra 2 +(h Tr+/,*,)e(r8 S)+(h8 Char$e8 D,e8 7+((+*/er8 Pre*(+ce Ha$$8 20098 a/e 51-569



A!#ace! A$/e&ra8 Tr+/,,)e(r8 a! S(a(+(+c8 R%+#+#ar8 S+& P%&$+h+/ H,%e8 2018 a/e

1J0-296

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