Multiple Choice
Identify the
choice that best completes the statement or answers the question.
|
|
|
1.
|
Evaluate the function  at  . Round to 3 decimal places.
a. | 54,270.000 | b. | 2.454 | c. | 303.008 | d. | 736.228 | e. | 803.695 |
|
|
|
2.
|
What is the value of the function 
at  ? Round to 3 decimal places.
a. | 1.398 | b. | 0.676 | c. | 1.795 | d. | –7.747 | e. | 0.848 |
|
|
|
3.
|
Let Q represent a mass of radioactive radium
(226Ra) (in grams), whose half-life is 1599 years. The quantity of radium present after
t years is
Determine the quantity present after 300 years. Round to the nearest hundredth
of a gram.
a. | 5.00 g | b. | 0.47 g | c. | 4.39
g | d. | 0.00 g | e. | 0.88 g |
|
|
|
4.
|
Rewrite the exponential equation 
in logarithmic form.
|
|
|
5.
|
Evaluate the function  at  . Round to 3 decimal places. (You may use your calculator.)
a. | –3.391 | b. | undefined | c. | –2.928 | d. | 2.150 | e. | 3.391 |
|
|
|
6.
|
Identify the x-intercept of the function
 .
a. |  | b. | The function has
no x-intercept. | c. |  | d. |  | e. |  |
|
|
|
7.
|
Solve the equation  for x
using the One-to-One Property.
a. | –9 | b. | –11 | c. | 0 | d. | The equation has
no solution. | e. | 11 |
|
|
|
8.
|
Rewrite the logarithm  in terms of
the common logarithm (base 10).
|
|
|
9.
|
Evaluate the logarithm  using the
change of base formula. Round to 3 decimal places.
a. | 0.630 | b. | 0.273 | c. | –0.692 | d. | –1.745 | e. | –0.573 |
|
|
|
10.
|
Simplify the expression  .
a. | The expression cannot be
simplified. | b. |  | c. |  | d. | 6 | e. |  |
|
|
|
11.
|
Find the exact value of  without
using a calculator.
|
|
|
12.
|
Condense the expression  to the
logarithm of a single term.
|
|
|
13.
|
Condense the expression 
to the logarithm of a single term.
|
|
|
14.
|
Solve for x:  . Round to 3
decimal places.
a. | 13.291 | b. | 10.518 | c. | –3.794 | d. | –13.291 | e. | 7.587 |
|
|
|
15.
|
Solve for x:  . Round to 3
decimal places.
a. | 2.407 | b. | –1.362 | c. | 0.407 | d. | 1.362 | e. | no
solution |
|
|
|
16.
|
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. | 4.2% | b. | 100% | c. | 8.3% | d. | 3.6% | e. | 8.4% |
|
|
|
17.
|
An initial investment of $9000 grows at an annual
interest rate of 5% compounded continuously. How long will it take to double the
investment?
a. | 1 year | b. | 13.86 years | c. | 14.86
years | d. | 13.40 years | e. | 14.40 years |
|
|
|
18.
|
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. | 59.3 hours | b. | 94.5 hours | c. | 9.6
hours | d. | 57.5 hours | e. | 92.7 hours |
|
|
|
19.
|
Carbon dating presumes that, as long as a plant or
animal is alive, the proportion of its carbon that is 14C is constant. The amount of
14C in an object made from harvested plants, like paper, will decline exponentially
according to the equation  , where A represents the amount of
14C in the object, Ao represents the amount of 14C in living
organisms, and t is the time in years since the plant was harvested. If an archeological
artifact has 40% as much 14C as a living organism, how old would you predict it to be?
Round to the nearest year.
a. | 87 years | b. | 16,006 years | c. | 30,411
years | d. | 7554 years | e. | 5715 years |
|
|
|
20.
|
The chemical acidity of a solution is measured in
units of pH:  , where  is the
hydrogen ion concentration in the solution. If a sample of rain has a pH of 3.2, how many times
higher is its  than pure water's, which has a pH of
7?
|