There were no jackrabbits in Australia before 1788 when 24 jackrabbits were introduced. By 1920 the population of jackrabbits had reached 10 billion. If the population had grown exponentially, this would correspond to a 16.2% increase, on average, in the population each year. Which of the following functions best models the population of jackrabbits t years after 1788?
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A
-
B
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C
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D
Correct answer: C
Explanation
Choice C is correct. This exponential growth model can be written in the form , where
is the population t years after 1788, A is the initial population, and r is the yearly growth rate, expressed as a decimal. Since there were 24 jackrabbits in Australia in 1788,
. Since the number of jackrabbits increased by an average of 16.2% each year,
. Therefore, the equation that best models this situation is
.
Choices A, B, and D are incorrect and may result from misinterpreting the form of an exponential growth model.
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