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Please help and show all your work for all the questions. Thank you!Exponential and Logarithmic Functions Unit Test
Nayrouz Bachir­Belmehdi is taking this assessment.
Multiple Choice
1. Which graph best represents y = 2x + 1? (1 point)
2. Some investments in the stock market have earned 10\% annually. At this rate, earnings can be (1 point)
found using the formula
, where A is the total value of the investment, P is the
initial value of the investment, and n is the number of years the money is invested. If \$1,500 is
invested in the stock market at this annual rate of return, what is the expected total value after
18 years?
\$29,700.00
\$28,050.00
\$8,339.88
\$7,581.71
3. Graph the logarithmic function. (1 point)
y = log(x – 3)
4. Expand the logarithmic expression. (1 point)
5. What is the value of log648? (1 point)
3
2
6. Solve the exponential equation. (1 point)
1258x–2 = 150
–0.1203
0.3797
0.3705
2.1297
7. Solve log(2x + 3) = 3. (1 point)
500
997
8. What is the percent rate of change in function y = (0.98)x? Determine whether the function
represents exponential growth or exponential decay.
2\%; exponential growth
20\%; exponential growth
2\%; exponential decay
0.2\%; exponential decay
(1 point)
9. Use natural logarithms to solve the equation. Round to the nearest thousandth. (1 point)
3e2x+ 2 = 28
1.0797
0.4689
0.9261
2.1595
10. Write the expression as a single logarithm. (1 point)
5logby + 4logbx
logb(y5 + x4)
logb(y5x4)
(5 + 4) logb(y + x)
logb(yx5 + 4)
11.
The exponential decay graph shows the expected depreciation for a new boat, selling for
\$3,500, over 10 years.
Write an exponential function for the graph. Use the function to find the value of the boat after
9.5 years.
(2 points)
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12. Write the equation in logarithmic form. (2 points)
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13.
Evaluate the logarithm.
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(2 points)
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14. Solve 1n2 + 1nx = 5. Round to the nearest thousandth, if necessary. (2 points)
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15. In a particular region of a national park, there are currently 330 deer, and the population is
increasing at an annual rate of 11\%.
a. Write an exponential function to model the deer population.
b. Explain what each value in the model represents.
c. Predict the number of deer that will be in the region after five years. Show your work.
(3 points)
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16. Describe how the graph of y = 2log (x – 4) + 2 compares to the parent graph. Discuss any
3
changes in the asymptotes, domain, and range.
(4 points)
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