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The population of squirrels in a park has been doubling ever...
PSAT PSAT-math-test math
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The population of squirrels in a park has been doubling every 15 years. Which of the following statements describes the type of function that best models the relationship between the population of squirrels in the park and the number of 15-year time periods?

A) Exponential growth, because the population of squirrels is increasing by the same amount each 15-year time period

B) Exponential growth, because the population of squirrels is increasing by the same percentage each 15-year time period

C) Linear growth, because the population of squirrels is increasing by the same amount each 15-year time period

D) Linear growth, because the population of squirrels is increasing by the same percentage each 15-year time period

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adeb
Asked by adebrep:453
School not set Nigeria
11 January 2021

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judziy
Judziy answeredrep:1.9K
University of Benin Nigeria
11 January 2021
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Let x be the initial population of Squirrels in the park, n be the number of 15-year time period, and p(n) be the population of Squirrels after n 15-years-time period.

Since the population of squirrels in the park has been doubling every 15 years, it means that if the current population of squirrels is x, 15 years later it will be, x(2)

Similarly, the population of Squirrels in the park 30, 45, and 60 years later will be, x(2)(2), x(2)(2)(2), x(2)(2)(2)(2) respectively.

The above populations after 15, 30, 45, and 60 years can be written as:

x(2)1, x(2)2, x(2)3 and x(2)4 respectively.

we could therefore express the population for n number of 15-years using a general form:

p(n) = x(2)n/15 ------------- eqn(1)

where n is in the range of 15 years, e.g: 15, 30, 45, 60...

We can clearly see from eqn(1) that the relationship between the population of squirrels in the park, p(n), and the number of 15-year time period, n, is growing exponentially and increasing by the same percentage, n/15, each 15-year time period

Answer: B

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