Exam 4 Review
Approximate the number using a calculator. Round your answer to three decimal places.
1) 2 1.7
2) e-1.4
Use the compound interest formulas A = P 1 +
r nt
and A = Pe rt to solve.
n
3) Find the accumulated value of an investment of $10,000 at 4% compounded semiannually for 5 years.
4) Find the accumulated value of an investment of $5000 at 5% compounded monthly for 8 years.
The graph of an exponential function is given. Select the function for the graph from the functions listed.
5)
Graph the function.
6) Use the graph of f(x) = 2 x to obtain the graph of g(x) = -2 x.
1
7) Use the graph of f(x) = ex to obtain the graph of g(x) = ex - 2.
Write the equation in its equivalent exponential form.
8) log 32 = x
2
Write the equation in its equivalent logarithmic form.
9) 5 3 = x
10) 7 x = 343
Evaluate the expression without using a calculator.
11) log9 81
12) log
27
13) log6
3
1
6
14) log 8 20
8
The graph of a logarithmic function is given. Select the function for the graph from the options.
15)
2
Graph the function.
16) Use the graph of log x to obtain the graph of f(x) = 2 + log x.
4
4
Find the domain of the logarithmic function.
17) f(x) = log (x - 2)
4
18) f(x) = ln (2 - x)
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
19)
5 4
log3 x y
9
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.
20) log (x + 3) - log (x + 6)
3
3
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
3
21) ln ey
22) log
6
x-6
x8
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.
23) 9ln a - 7 ln b
24)
1
(log4 x + log4 y) - 3 log4 (x + 7)
4
Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places
25) log 63.2
12
3
26) log
0.1
17
Solve the equation by expressing each side as a power of the same base and then equating exponents.
1
27) 3 (6 - 3x) =
27
28) 4 x + 2 = 8 x - 6
Solve the exponential equation. Express the solution set in terms of natural logarithms.
x+5
=2
29) e
30) 4 x + 4 = 5 2x + 5
Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the
solution.
31) e2x - 3 - 4 = 1402
32) e2x + ex - 6 = 0
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.
33) log (x + 2) = -1
6
34) 7 + 3 ln x = 15
35) log2 (x + 4) - log2 (x - 2) = 2
36) log 3x = log 4 + log (x - 1)
37) ln (x - 2) - ln (x + 2) = ln (x - 9) - ln (x + 4)
Solve.
38) 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 = 5100e0.057t. How much did you initially invest in the account?
39) The function A = A0 e-0.01386x 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 300 pounds of the
material are placed in the vault, how much time will need to pass for only 38 pounds to remain?
40) The population of a certain country is growing at a rate of 1.9% per year. How long will it take for this country's
ln 2
population to double? Use the formula t =
, which gives the time, t, for a population with growth rate k, to
k
double. (Round to the nearest whole year.)
4
41) The population of a particular country was 25 million in 1982; in 1992, it was 35 million. The exponential
growth function A =25ekt describes the population of this country t years after 1982. Use the fact that 10 years
after 1982 the population increased by 10 million to find k to three decimal places.
Solve the system of equations by the substitution method.
42)
-5x + 3y = -22
x - 5y = 0
43) 5x - 3y = 49 - 5x
3x + 7y = x + 6y + 5
Solve the system by the addition method.
44) 2x + 7y = 12
2x + 2y = 22
Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
45) 3x + y = 8
9x + 3y = 24
46) x + 3y = -2
2x + 6y = -4
Solve the system of equations.
47) x + y + z = 1
x - y + 5z = 13
5x + y + z = -19
48)
x +y+ z=1
x - y + 5z = -21
2x + 2y + 2z = 3
49) x - y + 5z = -3
4x
+ z=0
x + 3y + z = 9
50)
x +y
= -3
3x - 3y + 2z = 11
- z = -5
x
5
Answer Key
Testname: COLLEGE ALGEBRA TEST 4 REVIEW
1)
2)
3)
4)
3.249
0.247
$12,189.94
$7452.93
5) f(x) = 2 x
6)
7)
8) 2 x = 32
9) log x = 3
5
10) log 343 = x
7
11) 2
1
12)
3
13) -
1
2
14) 20
15) f(x) = log (x - 2)
4
6
Answer Key
Testname: COLLEGE ALGEBRA TEST 4 REVIEW
16)
17) (2, )
18) (- , 2)
4
1
2
19) log3 x + log3 y 5
5
5
20) log
21)
x+3
3 x+6
1
1
ln y +
3
3
22) log (x - 6) - 8 log x
6
6
a9
23) ln
b7
24) log4
4
xy
(x + 7)3
25)
26)
27)
28)
29)
1.6686
-1.2304
{3}
{22}
{ln 2 - 5}
5 ln 5 - 4 ln 4
30)
ln 4 - 2 ln 5
31) 5.12
32) 0.69
11
33) 6
34) e
35) {4}
36) {4}
37) 38)
39)
40)
41)
8/3
10
9
$5100.00
149 years
36 years
0.034
7
Answer Key
Testname: COLLEGE ALGEBRA TEST 4 REVIEW
42)
43)
44)
45)
46)
47)
48)
49)
50)
{(5, 1)}
{(4, -3)}
{(13, -2)}
{(x, y) 3x + y = 8}
{(x, y) | x + 3y = -2}
{(-5, 2, 4)}
{(0, 3, 0)}
{(-1, -2, 4)}
8