Name:    Chapter 3 Post Test

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.
 a. b. c. d. e.

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).
 a. b. c. d. e.

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.
 a. 2.5 b. 1.25 c. 2 d. 5 e. 3

12.

Condense the expression to the logarithm of a single term.
 a. b. c. d. e.

13.

Condense the expression to the logarithm of a single term.
 a. b. c. d. e.

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?
 a. b. c. d. e. 7