Chapter 4 Test Review
Analysis
Name___________________________________
Date _________________ Period____________
Graph the function by making a table of coordinates.
1x
1) f(x) =
5
6
1)
y
4
2
-6
-4
-2
2
4
6 x
-2
-4
-6
Graph the function.
2) Use the graph of f(x) = 2x to obtain the graph of g(x) = 2x + 1 + 1.
6
2)
y
4
2
-6
-4
-2
2
4
6 x
-2
-4
-6
Solve the problem.
3) A sample of 1000 g of lead-210 decays to polonium-210 according to the function given by
A(t) = 1000e-0.032t, where t is time in years. What is the amount of the sample after 40 years
(to the nearest g)?
A) 16 g
B) 3597 g
Use the compound interest formulas A = P 1 +
C) 202 g
3)
D) 278 g
r nt
and A = Pert to solve.
n
4) Suppose that you have $9000 to invest. Which investment yields the greater return over 8
years: 7.5% compounded continuously or 7.6% compounded semiannually?
A) $9000 invested at 7.6% compounded semiannually over 8 years yields the greater return.
B) Both investment plans yield the same return.
C) $9000 invested at 7.5% compounded continuously over 8 years yields the greater return.
1
4)
Write the equation in its equivalent exponential form.
5) log b 25 = 2
A) 252 = b
5)
B) b2 = 25
Write the equation in its equivalent logarithmic form.
3
6) 8 = 2
1
A) log 2 8 = 3
B) log 2 8 =
3
C) 2b = 25
D) 25b = 2
1
C) log 8 3 =
2
1
D) log 8 2 =
3
6)
Evaluate the expression without using a calculator.
7) log2 32
A) 5
8) log9
7)
B) 2
C) 10
D) 32
1
9
A) -
8)
1
9
B)
1
9
C)
1
2
D) -
1
2
9) log 3 3
9)
A) 0
B) 1
C)
1
3
D) 3
Graph the functions in the same rectangular coordinate system.
10) f(x) = 3x and g(x) =log3x
10)
y
6
6 x
-6
-6
Evaluate the expression without using a calculator.
1
11) ln
e4
A)
1
4
B) -
11)
1
4
C) -4
2
D) 4
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
12) log 4 (16x)
12)
A) 2 + log 4 x
B) 2x
C) 2 log 4 x
D) 8 + log 4 x
27
13) log 3
x
13)
A) - 3 log 3 x
B)
3
x
C) 9 - log 3 x
14) logb (yz4)
A) 4 logb y + 4 logb z
14)
B) 4 logb yz
C) logb y + 4 logb z
D) logb y + logb4z
x-8
x8
15) log 5
15)
A) log 5 (x - 8) + 8 log 5 x
C) 8 log 5 x - log 5 (x - 8)
5
16) log 9
A)
D) 3 - log 3 x
B) log 5 (x - 8) - log 5 x
D) log 5 (x - 8) - 8 log 5 x
4
m n
k2
16)
5
4
2
log 9 m + log 9 n - log 9 k
9
9
9
C) 5 log 9 m + 4 log 9 n - 2 log 9 k
B)
1
1
log 9 m + log 9 n - 2 log 9 k
5
4
D)
1
1
log 9 m · log 9 n ÷ 2 log 9 k
5
4
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm
whose coefficient is 1. Where possible, evaluate logarithmic expressions.
17) 5 log b m - log b n
17)
18)
m5
A) log b
n
5m
B) log b (
)
n
C) log b (m5 - n)
D) log b m5 ÷ log b n
1
log8x + log8y
2
A) log8 xy
18)
B) log8
x
y
x
C) log8
y
D) log8y x
19) 7ln (x - 4) - 8 ln x
A) ln 56x(x - 4)
19)
B) ln x8(x - 4)7
C) ln
3
(x - 4)7
x8
D) ln
7(x - 4)
8x
Solve the equation by expressing each side as a power of the same base and then equating exponents.
1
20) 3(3x + 6) =
27
A) {9}
21) 2x = 16
A) {4}
B)
1
9
C) {-3}
20)
D) {3}
21)
B) {8}
C) {3}
D) {5}
Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places,
for the solution.
22) 4x = 12
22)
A) 0.56
23) 2 x + 7 = 4
A) -0.54
B) 3.44
C) 1.79
D) 0.65
B) 1.35
C) -5.00
D) 7.50
23)
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
24) log 3 x = 5
24)
A) {125}
B) {1.46}
C) {15}
D) {243}
25) log 4 (x + 2) + log 4 (x - 4) = 2
A) {6}
B) {7}
25)
C) {-4}
D) {6, -4}
26) log (x + 4) = log (5x - 5)
9
A)
5
9
B)
4
9
C) 4
1
D)
4
20
B) 9
1
C)
3
26)
27) log 4x = log 5 + log (x - 4)
A) {-20}
27)
D) {20}
Solve.
28) The value of a particular investment follows a pattern of exponential growth. In the year 2000,
you invested money in a money market account. The value of your investment t years after
2000 is given by the exponential growth model A = 4200e0.058t. When will the account be
worth $5297?
A) 2005
B) 2004
C) 2003
D) 2006
29) The function A = A0e-0.00866x models the amount in pounds of a particular radioactive
material stored in a concrete vault, where x is the number of years since the material was put
into the vault. If 200 pounds of the material are initially put into the vault, how many pounds
will be left after 90 years?
A) 89 pounds
B) 108 pounds
C) 92 pounds
D) 113 pounds
4
28)
29)
Answer Key
Testname: TEST 4 REVIEW
1)
y
6
4
2
-6
-4
-2
2
4
6 x
2
4
6 x
-2
-4
-6
2)
y
6
4
2
-6
-4
-2
-2
-4
-6
3) D
4) C
5) B
6) D
7) A
8) D
9) B
10)
y
6
6 x
-6
-6
11)
12)
13)
14)
C
A
D
C
5
Answer Key
Testname: TEST 4 REVIEW
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
D
B
A
D
C
C
A
C
C
D
A
B
D
B
C
6