'-= -

Unit 3 Review - EXPONENTIALS

1. Gina sells cell phone covers. The revenue, R dollars, earned in a week is R = P(241- 19P), where Pdollars is the price she charges per cover. Determine the revenue earned in a week if she charges$4 per cover. R ~ Jf (:141-/ q (tf) ) Q\ i' ideO wC0a (1tVJ ~ ~ C!'YU- (.t~-

=-!f( fhr)z: ft,roo R = M

2. The price-earnings ratio, R, of a company is given by the equation E, where M is the marketvalue per share and Eis the earnings per share for the last year.a) Isolate M. I<::=- m' Cl)f R =- M K6- ~) E R z: ~ jJ eb) Isolate E. t=:: . z f~ml

J ~rz = MJ tf-= ~ /; «.p=-

3. The power, P, of an engine is given by the equation 9549, where Tis the engine's torque and Ris

the rotations per minute. p= iR ,,/.,r'ljf zz: Tf. (~r~ b) r%'Iq p z: rz7a) Isolate T. 05+1 - LT )b) IsolateR. ~ 71' = T --~

4. Roma's weekly earnings, Edollars, are given by e e a Ion = 23R+ 34.50, where Ris the number ofregular hours she works and 0 is the number of overtime hours she works. Determine the number ofovertime hours Roma works if she earns $960.25 endworks 33.5 regular hours. :7- tru-eu: .

5. The speed, Smetres per second, of a falling object dropped from rest can be estimated by the

formula S = ~, where h metres is the distance the object falls. Determine the distance that anobject travelling at 20 m/s has fallen, assuming that it was dropped from rest.

4R3

L=-26. The length, L, of rope in a ball of rope may be estimated using the formula 3c, where R is the

radius of the ball and c is the cross-sectional radius of rope. Rearrange the formula to isolate c.

, ~9. A sample of iodine-125 undergoes radioactive decay. The equation M = 45(1.012) gives the mass M g

of iodine-125 remaining after tdays. Determine the initial mass of iodine-125 and the massremaining after 50 days. C\) (" ihCxJ... (Y)~:::: Jf5 2 h) M::: tf.C)( I, 0/2) -50

(; z: :2t./- g ,/1--& r;0 da.er10. Explain the meaning of the exponent in the expression 64 . ----z ~~5 a_r~' _

tne.anv: -1-0 kh flU! bofA rool: Q} foLfV I r

11. Rewrite -0.343 using rational exponents and evaluate. ------------ _-I

-D,~4-33 ~ -0.7.

4 3 1- o I _t? 0 [= LI-~12. Solve for x in the equation x = 81. Assume x is positive. ::::-6 ~ r- r _~-----------~~-------------------a,

13. Solve the equation 32/: = 9 algebraically. c2~ -:=: a (> 'f..- z: 2-

3/,' = ~ 1~ )---:-x---514. Use systematic trial to solve the equation 17 . Round to 2 decima pace . -~'=======~ _

br-er ):>.

15. Suppose you invest $800 at 6.7% a year, compoundedcnnuclly. After n years, the amount of the

investment is given by A = 800(1.067l. Write an equction that can be used to 'determine how long ittakes for the investment to grow to $1600.

16. The population Pof a new town doubles every 26 months. Write an equation that models thepopulation n months after the town had a population of 1700.

18. a) Rewrite using radicals and evaluate.2 3 4- - -

i) 42 ii) 83

iii) 164

b) Is there a simpler way to evaluate these powers? Explain your reasoning.c) Evaluate.

2

i) 92

4

iii) 81 4

17. The number of bacteria in a colony can be modelled by the equation B = 1500(2.6)11 , where B is thenumber of bacteria and n is the number of hours from now.a) Determine the number of bacteria in the colony 2 h from now.b) Determine the number of bacteria in the colony now. Explain your reasoning.c) Determine the number of bacteria in the colony 2 h ago. Explain your reasoning.

19. Kleiber's Law states that the energy required per day, Pkilocalories, for an animal with mass M34

kilograms, is given by the formula P = T0M .a) Determine the energy required per day by a 1100 kg elephant.b) Determine the energy required per day by a 0.034 kg mouse.c) The energy required by a human is 2500 kcal per day. Determine its body mass.

Explain your strategy.

-=#-~. ~= ;23R of 31-,5 0

CJbO,;)S = ~3 (s:?<~)-t 311, S" D0IoDl~) z: ~ 77o. r; -J- ~ if; r 0 .

qfd).J~-77o,t) = 3~ 0 .

3q,r:; 3%

------< f. J)Lt ILL~ Ct.r KU L-J--; LUa.-o

ch ~ ~ L-!JCt4 ~

dO. Lfl/Yl .

~5- S z: fiq. ~ h S:::- :;0 Yhlr; 0

JD = --({q){ K R 0

~ -VlyL.__ -rr-;-;:::::::::::;-r:;2

~f~~~~QTl

-(g'X::: /1

~-'.

gY- co. D,Q5~.? ~ fu ~ oi 'X ~ <@W'10 you I:-:J..

3 z: J ::-D,11 .)o.fl tJuumb-0r Lao h bL O1Mi0r ~ :2tfj {I

3-3~ I z: 0.03703 ~ ~ ~fL.-- h c: ~ L 3;)1

-:J. "-3 . :: Of o57tfJ

( ,-J5f V.) '" D. 05&7'5 .

-------- Ii

-:Itl(r, P ~ 1700 (;').) ~

-----,-B::: 1500 (!lie) r)

B:::- t500 {.9.(,,):L

B z: /D/'-I-o ~~--------

!3 = /600 ( .2. f.o) o --.

:= 15()o If)=- 11500 ~&r~J fvou...)

.-2./3= /£00 (:J.~)

= It;oo (D. /1-1-70)

:: ;);;2 ;.'1=- ;);) ;;;J bCl.-C-f er ~c.J

~ l~< e\) 4-% ~ ~ ::: d;J ::: if.

8~ ~ ~ ~ j-5 ~ $

.----------4f 1C1.~ fY' s: \ \ 00 k-j

3.

P::-loMtt. 3/t{

::::10 (\ IDO)

~ 70 (\q 1.0)

~ t3 310 k-cJ3/4P -:: 10 1'-\

'3N~ I oC b .O~lf)

= l O(O,O'lQa)

~ S-.54- kc-~