Pre-Calculus
Final Exam Review
Chapter 3
Name: ______________
Date: ______________
1. Identify the operation that will transform the graph of f ( x)  2 x into the graph of
g ( x)  3  2 x .
2. Use the One-to-One Property to solve the following equation for x.
1
 
3
7 x1
 27
3. A national retailer attempts to determine a demand curve for a new product by selling it
in different regions of the country for different prices. The resulting data is shown in the
table below.
Price ($)
Annual Demand/
10,000 population
2.00
230
2.50
134
3.00
78
3.50
46
4.00
27
The Vice President of Exponential Modeling determines that the demand can be
modeled by the function D( p)  1996.5 e–1.08 p , where p is the price in dollars and D(p)
is the annual demand per 10,000 population. Use the model equation to estimate the
demand if the price is set at $2.35.
4. Identify the x-intercept of the function y  4  log 4 x .
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5. The pH of an acidic solution is a measure of the concentration of the acid particles in the
solution, with smaller values of the pH indicating higher acid concentration. In a
laboratory experiment, the pH of a certain acid solution is changed by dissolving overthe-counter antacid tablets into the solution. In this experiment, the pH changes
according to the equation
x


pH  4.20  log 
,
0.35

x


where x is the number of grams of antacid added to the solution. What is the pH of the
solution after the addition of 0.3 grams of antacid tablet?
6. Evaluate the logarithm log1/ 3 1.093 using the change of base formula. Round to 3
decimal places.
7. Find the exact value of log 3 16 without using a calculator.
4
8. Expand the expression
as a sum, difference, and/or constant multiple of logarithms.
9.
Condense the expression
1
[log 4 x  log 4 6]  [log 4 y] to the logarithm of a single term.
5
10. Solve ln x2  ln 3  0 for x.
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11. Solve for x: e x (2  e x )  1 . Round to 3 decimal places.
12. Approximate the solution of 9e x – 5  10 to 3 decimal places. (You may use a graphing
utility.)
13. An initial investment of $4000 doubles in value in 10.9 years. Assuming continuous
compounding, what was the interest rate? Round to the nearest tenth of a percent.
14. What is the half-life of a radioactive substance if 2.4 g decays to 0.80 g in 66 hours?
Round to the nearest tenth of an hour.
15. A television rating company tracks the viewing habits of a select sample of American
TV viewers and extrapolates the results to estimate the total viewership of any particular
show. The estimate of the number of viewers of a particular new show over a period of
4 months was modeled as N (t )  108 ekt , where t represents the number of weeks since
the opening episode, and k is a constant. If there were 108,000 viewers for the first
episode and 2.25 million viewers 7 weeks later for the eighth episode, identify an
appropriate value for k. Round to the nearest thousandth.
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