Chapter 4 Review
I. The exponential function f(x) = 13.49(0.967)x - 1 describes the number of Orings expected to fail, f(x), when the temperature is xF. Find the number of Orings expected to fail at the given temperature.
1.
31F
2.
60F
3.
-10F
Graph.
4.
f  x  2
7.
1
f  x   
3
x
x
5.
g  x  3
8.
g  x   3x 1
x
x
6.
1
h  x   
2
9.
h  x   2x  3
10.
The function f(x) = 3.6e0.02x describes world population, f(x), in billions, x
years after 1969. Find the world population in 2020.
11.
The function f(x) = 6.4e0.0123x describes world population, f(x), in billions, x
years after 2004. Find the world population in 2050.
12.
You decide to invest $8000 for 6 years. How much will have if you invest at
7% per year, compounded monthly? at 6.85% per year, compounded continuously?
13.
You decide to invest $10000 for 5 years at an annual rate of 8%. How much
will have if it is compounded quarterly? compounded continuously?
CAT Ch4 Review, 3/31/2011
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Chapter 4 Review
II.
Write each equation in its equivalent exponential form:
14.
2 = log5x
15.
3 = logb64
16.
log37 = y
Write each equation in its equivalent logarithmic form:
17.
122 = x
18.
b3 = 8
19.
ey = 9
Evaluate.
20.
log216
21.
log39
22.
log255
23.
log77
24.
log51
25.
log778
26.
6log69
27.
log445
28.
log81
33.
f(x) = ln (3 - x)
Graph.
29.
f(x) = log2x
Find the domain.
31.
f(x) = log4 (x + 3)
34.
30.
32.
g(x) = log3x
g(x) = log4 (x - 5)
g(x) = ln (x - 3)2
35.
The percentage of adult height attained by a boy who is x years old can be
modeled by f(x) = 29 + 48.8 log (x + 1), where x represents the boy’s age and f(x)
represents the percentage of his adult height. An 8 year old boy has attained
approximately what percentage of his adult height?
36.
The function f(x) = 13.4 ln x - 11.6 models the temperature increase, f(x), in
degrees Fahrenheit, after x minutes in an enclosed vehicle. Find the temperature
increase after 50 minutes.
CAT Ch4 Review, 3/31/2011
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Chapter 4 Review
III.
Expand each expression.
37.
log4(7• 5)
38.
log (10x)
39.
log574
42.
ln x
45.
 3x 
log 6 
4 

 36 y 
40.
 19 
log 7  
 x
41.
 e5 
ln  
 11 
43.
log (4x)5
44.
logb x 2 y


Write as a single logarithm.
1
log x  4log  x  1
2
46.
log42 + log432
47.
log (4x - 3) - logx 48.
49.
3 ln (x + 7) - ln x
50.
1
4logb x  2logb 6  logb y
2
Evaluate.
51.
log5140
52.
log72506
IV
Solve.
53.
23x-8 = 16
54.
27x+3 = 9x-1
55.
4x = 15
56.
40e0.6x - 3 = 237
57.
5x-2 = 42x+3
58.
e2x - 4ex + 3 = 0
59.
log4 (x + 3) = 2
60.
3 ln (2x) = 12
61.
log2 x + log2 (x - 7) = 3
62.
1
ln  x  2   ln  4 x  3  ln  
 x
CAT Ch4 Review, 3/31/2011
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Chapter 4 Review
63.
The risk of having a car accident while under the influence of alcohol can be
modeled by R = 6e12.77x, where x is the blood alcohol concentration and R, given as a
percent, is the risk of a car accident. What blood alcohol level corresponds to a
20% risk of a car accident?
64.
How long will it take $25,000 to grow to $500,000 at 9% annual interest
compounded monthly?
 r
A  P 1  
 n
nt
65.
The function f(x) = 34.1 ln x + 117.7 models the number of U.S. Internet
users, f(x), in millions, x years after 1999. By what year will there be 200 million
Internet users in the U.S.?
V.
66.
In 1970, the U.S. population was 203.3 million. By 2003, it had grown to 294
million. Find the exponential growth function that models this data (A = A 0ekt).
Then find the year when the population will reach 315 million.
67.
Use the fact that after 5715 years a given amount of carbon-14 will have
decayed to half the original amount to find the exponential decay model for
carbon-14. Then estimate the age of scrolls found in 1947 that contained 76% of
their original carbon-14.
30000
describes the number of people, f(t), who have
1  20e1.5t
become ill with influenza t weeks after its initial outbreak in a town with 30,000
inhabitants. How many people became ill when the epidemic began? How many
people were ill by the end of the fourth week? What is the limiting size of f(t),
the population that becomes ill?
68.
The function f (t ) 
69.
Rewrite y = 2.557 (1.017)x in terms of base e.
CAT Ch4 Review, 3/31/2011
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