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m1314c4
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Evaluate the function
a. 4.680
b. 20.055
c. 1.690
d. 2.572
e. 5.287
at
. Round to 3 decimal places.
____
2. What is the value of the function
a. 1.795
b. 0.676
c. 0.848
d. –7.747
e. 1.398
____
3. What is the value of the function
a. 42.051
b. 82.783
c. 26.492
d. 37.296
e. 7.597
____
4. Use the One-to-One Property to solve the following equation for x.
at
at
? Round to 3 decimal places.
? Round to 3 decimal places.
a.
b.
c. 2
d.
e.
____
5. Use the One-to-One Property to solve the following equation for x.
a.
b.
c.
d.
e.
____
6. Rewrite the logarithmic equation
in exponential form.
a.
b.
c.
d.
e.
____
7. Rewrite the exponential equation
in logarithmic form.
a.
b.
c.
d.
e.
____
8. Evaluate the function
at
without using a calculator.
a. 27
b. –4
c. –2
d.
e. –3
____
9. Identify the value of the function
a. 3.118
b. 6.028
c. 4.118
d. 3.618
e. 2.618
____ 10. Write the logarithmic equation
at
. Round to 3 decimal places.
in exponential form.
a.
b.
c.
d.
e.
____ 11. Write the exponential equation
a.
in logarithmic form.
b.
c.
d.
e.
____ 12. Evaluate the function
at
. Round to 3 decimal places. (You may use your
calculator.)
a. 0.876
b. 0.339
c. undefined
d. –0.347
e. 0.147
____ 13. Identify the x-intercept of the function
a.
b.
c.
d. The function has no x-intercept.
e.
____ 14. Solve the equation
a. 0
b. –11
c. The equation has no solution.
d. 11
e. –9
____ 15. Rewrite the logarithm
a.
b.
.
for x using the One-to-One Property.
in terms of the common logarithm (base 10).
c.
d.
e.
____ 16. Rewrite the logarithm
a.
in terms of the natural logarithm.
b.
c.
d.
e.
____ 17. Evaluate the logarithm
a. 3.738
b. 1.921
c. 1.623
d. 7.273
e. 0.521
____ 18. Evaluate the logarithm
a. 0.273
b. –0.692
c. –1.745
d. 0.630
e. –0.573
using the change of base formula. Round to 3 decimal places.
using the change of base formula. Round to 3 decimal places.
____ 19. Simplify the expression
.
a. 6
b. The expression cannot be simplified.
c.
d.
e.
____ 20. Find the exact value of
a.
b.
c.
without using a calculator.
d.
e. –1
____ 21. Simplify the expression
a.
b.
c.
d.
e.
.
–108
4
1
The expression cannot be simplified.
–12
____ 22. Find the exact value of
a. 2.5
b. 3
c. 2
d. 5
e. 1.25
without using a calculator.
____ 23. Find the exact value of
a.
without using a calculator.
b. 4
c. 1
d.
e. 9
____ 24. Condense the expression
to the logarithm of a single term.
a.
b.
c.
d.
e.
____ 25. Condense the expression
a.
b.
c.
to the logarithm of a single term.
d.
e.
____ 26. Condense the expression
to the logarithm of a single term.
a.
b.
c.
d.
e.
____ 27. Determine whether or not
is a solution to
.
a. no
b. yes
____ 28. Solve
a.
b.
c.
d.
e.
for x.
-1
-3
1
-5
no solution
____ 29. Solve for x:
a. 10.518
b. –3.794
c. 7.587
d. –13.291
e. 13.291
. Round to 3 decimal places.
____ 30. An initial investment of $3000 doubles in value in 8.3 years. Assuming continuous compounding,
what was the interest rate? Round to the nearest tenth of a percent.
a. 8.4%
b. 100%
c. 4.2%
d. 3.6%
e. 8.3%
____ 31. The population P of a bacteria culture is modeled by
, where t is the time in hours. If the
population of the culture was 5800 after 40 hours, how long does it take for the population to
double? Round to the nearest tenth of an hour.
a. 57.5 hours
b. 94.5 hours
c. 59.3 hours
d. 9.6 hours
e. 92.7 hours
____ 32. Determine the order of the matrix.
a.
b.
c.
d.
e.
31
33
23
32
22
____ 33. If possible, find 2A – 5B.
a. not possible
b.
c.
d.
e.
____ 34. If possible, find AB.
a. not possible
b.
c.
d.
e.
____ 35. Find the determinant of the matrix
a.
b.
c.
d.
e.
–63
–12
22
–33
6
____ 36. Given
a.
b.
c.
d.
e.
.
88
40
–80
168
–120
, find
.
m1314c5
Answer Section
MULTIPLE CHOICE
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35.
ANS:
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D
PTS: 1
OBJ: Raise number to a non-integer power
A
PTS: 1
OBJ: Evaluate exponential functions
A
PTS: 1
OBJ: Evaluate exponential functions
A
PTS: 1
OBJ: Solve exponential equations using one-on-one property
E
PTS: 1
OBJ: Solve exponential equations using one-on-one property
D
PTS: 1
OBJ: Express logarithmic equation in exponential form
E
PTS: 1
OBJ: Express exponential equation in logarithmic form
E
PTS: 1
OBJ: Evaluate logarithmic function
E
PTS: 1
OBJ: Evaluate logarithmic function
A
PTS: 1
OBJ: Express logarithmic equation in exponential form
C
PTS: 1
OBJ: Express exponential equation in logarithmic form
E
PTS: 1
OBJ: Evaluate logarithmic function
E
PTS: 1
OBJ: Identify x-intercept of logarithmic function
E
PTS: 1
Solve logarithmic equations using the one-on-one property
E
PTS: 1
OBJ: Convert logarithmic expression from one base to another
D
PTS: 1
OBJ: Convert logarithmic expression from one base to another
B
PTS: 1
OBJ: Evaluate logarithm using change of base formula
E
PTS: 1
OBJ: Evaluate logarithm using change of base formula
D
PTS: 1
OBJ: Simplify logarithmic functions
C
PTS: 1
Evaluate logarithmic function using properties of logarithms
E
PTS: 1
OBJ: Simplify logarithmic functions
C
PTS: 1
Evaluate logarithmic function using properties of logarithms
C
PTS: 1
Evaluate logarithmic function using properties of logarithms
E
PTS: 1
Condense logarithmic function using the properties of logs
C
PTS: 1
Condense logarithmic function using the properties of logs
C
PTS: 1
Condense logarithmic function using the properties of logs
A
PTS: 1
OBJ: Check the solution to an exponential equation
B
PTS: 1
OBJ: Solve exponential equations
C
PTS: 1
OBJ: Solve exponential equations
A
PTS: 1
OBJ: Solve exponential equations
E
PTS: 1
OBJ: Solve exponential equations
C
PTS: 1
OBJ: Determine order of matrix
E
PTS: 1
OBJ: Add and subtract matrices
A
PTS: 1
OBJ: Multiply matrices
D
PTS: 1
OBJ: Find the determinant of a matrix
36. ANS: D
PTS: 1
OBJ: Find the determinant of a matrix