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Pre-Ca lculus (2003-4)Review for Tes t Chapter 3

Compute the exact value of the function for the given x-value.

1. f(x)=7.2xforx=1 2. f(x)=2.144x for

3. f(x )=6 .9xforx=_ 4. f(x)=4.27x for

Write the exponential function that satisfies the given conditions.5. Ini tial population = 354, doubling every 6 hours. çtC)

6. Initial population = 1,426 , tripl ing every 9 hours. ço’ 4(’ (‘b .) ‘

7. Initial mass = 4,598 grams, increasing at a rate of 2.7% ccC) ‘.s2 i.oaiY8. Initial mass 785 grams, decsing at a rate of 3.7% ccc

the log ari thm ic express ion by riting it into exponential form.

iogT=x XI] 10. 1og2=x c= 6/S 11.

15. 1og2=x ‘5 16. log =x V-Ic5!10 00

19. log 1,000 = x 20. In e = x q

21. In[_) x - 22. log lOO, 000, 000 = x 23.

Write the expression log x using only common logarithms.

Write the expression 1og x using only common logarithms.

Write the express ion log (a — 6b) using only natural logarithms.

Write the expression log (2a + 8b) using only natural logarithms.

Assuming x and y are positive, use properti es of logarithms to write the expression as sum or difference oflogarithms or multiple logarithms.

28. In(4] 7-j - 29. log Jx8y5

X4cX

Assuming x and y are positive , use properties of logarithms to write the expression as a single logarithm.

31 . 32. lnx+5Iny_!lnz 33. 2(lnx+lny)_!lnzI

____ ____

5 (

__

--logx+3loy—4logz‘cx t-’’_

Complete the given tab le and graph the function.

34 f(x)=log

x y

-1

i 0

L, 1

i-r1 r x y

°/g -2

a

L’

Solve

9.

12. logx=—3 13. lnx=2 7 €_

18. lnx=—4 X 3’

1log = x

14. logiT=x

24.

25.

26.

27.

17. logx=2 ‘cc

Inex X]

30. log (z2Jx5y8)

35. f(x)=logx—1)

.._...L....J.

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YOU MAY USE A CALCULATOR NamePre-Calculus (2003-4) ---Review for Test Chapter 3.1 — 3.

Determine a formula for the exponential function whosevalues are given in the table or whose graph is shown.1. 2.

x f(x)

-2 1.667

0 15

2 135

x f(x)

-2 10

0 22.5

2 50.625

4. The number P of students infected with flu t days after exposure is modeled by P(t)=

1+e -a) What was the initial number of students infected with the flu? -..-9b) How many students were infected after 2 days? “-O

C) When will 250 students be infected? .k dG.s *

d) What would be the maximum number of students infected?

5. The population of Metroville is 257,000 and is decreasing by 2.1% each year.a) Write a function that models the population as a function of time t. LO scc (b) Predict when the population will be 170,000. 413

6. The population of Preston is 86,000 and is increasing by 1.4% each year.a) Write a function that models the population as a function of time t. cct): co ( o 4)b) Predict when the population will be 92,000. 4 4 .u

Solve each equation algebraically. SHOW YOUR WORK!!! Obtain a numerical approximation for your solution.Round your answer to the thousandths.

8. 34e =178

10.32

=14 11. logx—3)—5=3 c’j

13. 36e =180 14. 2(8)6 =86 O’33

16. logx—4)+12=16 17. In(3x+1)I1n(x_2)=1n(2x2+4x_4) q--FT3

19. State whether the function y = ex_ —2 is an exponential growth or an exRonential decafuicion and

describe its end behavior using limits. Lcou —

20. State whether the function y = 2ex +4 is an exponential growth or an exponential decay function and

describe its end behavior using limits. Cc) 4 lC Ric)

For 21 & 22, graph the given function (be sure to plot at least 2 points exactly) and analyze it for its domain,range, asymptotes, and describe its end

21. f(x)=log4x)

3. Find the logistic function that satisfies thegiven conditions:

A) Initial value = 45, limit to growth = 450,

passing through (2, 225).-

‘

B) Initial value = 100, limit to growth = 700,passing through (2, 280)..

‘f .4-t(

7.(345)X

= 10.25 j%219

18. In(2x+4)+In(x_1)=ln(x2_10x+19) _i-4sq

9. 7(5) =94

12. 2.45x =9.25

15.5X+2

9 —

Domain:Rinnp

behavior using limits.

22 .

Asymptotes:End Behavior: b’ r ç’Cx.)

‘iw’ Etc)

i4 •L%.4

.1jL i:

f(x) = log (16x)

Domain: W>ORange:Asymptotes: 0

End Behavior: —

4i —

Li..

P

IL.iC