Exponential Growth Function

What are the domain and range of the function?

• The domain is the set of integers, and the range is y > 4.

• The domain is the set of integers, and the range is y > 0.

• The domain is the set of real numbers, and the range is y > 0.

• The domain is the set of real numbers, and the range is y > 4.

After years of maintaining a steady population of 32,000, the population of a town begins to grow exponentially. After 1 year and an increase of 8% per year, the population is 34,560. Which equation can be used to predict, y, the number of people living in the town after x years? (Round population values to the nearest whole number.)

• y = 32,000(1.08)x

• y = 32,000(0.08)x

• y = 34,560(1.08)x

• y = 34,560(0.08)x

A growth medium is inoculated with 1,000 bacteria, which grow at a rate of 15% each day. What is the population of the culture 6 days after inoculation?

• y = 1,000(1.15)6; 2,313 bacteria

• y = 1,000(1.15)7; 2,660 bacteria

• y = 1,000(1.5)5; 7,594 bacteria

• y = 1,000(1.5)6; 11,391 bacteria

Which equation represents an exponential function that passes through the point (2, 36)?

• f(x) = 4(3)x

• f(x) = 4(x)3

• f(x) = 6(3)x

• f(x) = 6(x)3

Which graph shows exponential growth?

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What is the rate of change of the function described in the table?

• 12/5

• 5

• 25/2

• 25

Ramon is graphing the function f(x) = 3(4)x. He begins by plotting the initial value. Which graph represents his initial step?

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Which is the graph of f(x) = 5(2)x?

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Which best describes the graph of the function f(x) = 4(1.5)x?

• The graph passes through the point (0, 4), and for each increase of 1 in the x-values, the y-values increase by 1.5.

• The graph passes through the point (0, 4), and for each increase of 1 in the x-values, the y-values increase by a factor of 1.5.

• The graph passes through the point (0, 1.5), and for each increase of 1 in the x-values, the y-values increase by 4.

• The graph passes through the point (0, 1.5), and for each increase of 1 in the x-values, the y-values increase by a factor of 4.

Geraldine is asked to explain the limits on the range of an exponential equation using the function f(x) = 2x. She makes these two statements:

1. As x increases infinitely, the y-values are continually doubled for each single increase in x.

2. As x decreases infinitely, the y-values are continually halved for each single decrease in x.

She concludes that there are no limits within the set of real numbers on the range of this exponential function. Which best explains the accuracy of Geraldine’s statements and her conclusion?

• Statement 1 is incorrect because the y-values are increased by 2, not

• Statement 2 is incorrect because the y-values are doubled, not halved

• The conclusion is incorrect because the range is limited to the set of integers.

• The conclusion is incorrect because the range is limited to the set of positive real numbers.