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Exponential and Logarithmic Functions — Test Answers

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An equation for the depreciation of a car is given by y is equal to cap A times open paren 1 minus r close paren to the t th power , where y is equal to current value of the car, cap A is equal to original cost, r is equal to rate of depreciation, and t is equal to time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10 percent Approximately how old is the car?

A
5 point 6 years
B
5 point 0 years
C
3 point 3 years
D
6 point 6 years
22
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Which graph represents an exponential decay function?

A
Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, passes through the points (negative 2 comma 0 point 2 5), (negative 1 comma 0 point 5), (0 comma 1), (1 comma 2), (2 comma 4) and (3 comma 8). The curve has a horizontal asymptote at y equals 0 (the x-axis), which it approaches as x approaches negative infinity.
B
Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, begins at approximately (0 comma 0) and extends to the right in fourth quadrant. The curve is continuously decreasing and it passes through approximately (1 comma negative 1), (4 comma negative 2), and (9 point 5 comma negative 3).
C
Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, begins at the origin (0 comma 0) and extends into the first quadrant. The curve is continuously increasing and appears concave down. It passes through (1 comma 1), (3 comma 2), and (8 comma 3).
D
Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, passes through the points (negative 1 comma 2), (negative 2 comma 4), (negative 3 comma 8), (0 comma 1), (1 comma 0 point 5), and (2 comma 0 point 2 5). The curve has a horizontal asymptote at y equals 0 (the x-axis), which it approaches as x approaches positive infinity.
23

Interpret the following exponential function: y is equal to 6 times 1 point 0 7 to the x th power What is the growth/decay factor? What is the y -intercept?

A
Growth factor is 6 ; y -intercept is 1 point 0 7
B
Growth factor is 1 point 0 7 ; y -intercept is 6
C
Decay factor is 6 ; y -intercept is 1 point 0 7
D
Decay factor is 1 point 0 7 ; y -intercept is 6
24

Which of the following describes the growth rate of the exponential function in the graph?

A
For each x increase of 1 , the y increases by doubling and then adding 1 .
B
For each x increase of 1 , the y increases by a common factor of 3 .
C
For each x increase of 1 , the y increases by a common difference of 3 .
D
For each x increase of 1 , the y increases by 4 more than the previous increase.
25

Use the values in the table to verify the relationship between the functions representing the investments. Which conclusion can be made?

A
The functions are not inverses because for each ordered pair open paren x comma y close paren for one function, there is no corresponding ordered pair open paren x comma y close paren for the other function.
B
The functions are not inverses because for each ordered pair open paren x comma y close paren for one function, there is no corresponding ordered pair open paren y comma x close paren for the other function.
C
The functions are inverses because the range of Table A is different from the domain of Table B.
D
The functions are inverses because the domain of Table A is the same as the range of Table B.

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