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A study of black bears in the Adirondacks reveals that their population can be represented by the function , where is the number of years since the study began. Write a function that models the monthly growth rate (to the nearest hundredth of a percent) of the black bear population

1 Answer

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Answer:


\mathbf{ P(t) = 3500 (1.}00206)^(12t)

Explanation:

The missing value of the given function is:


P(t) = 3500 (1.025)^t

where

t = no. of years since study began


P(t) = 3500 (1+0.025)^t

Per year, the function can be written as:


P(t) = 3500 (1+(25)/(1000))^t

For monthly growth rate m = 12


P(t) = 3500 (1+(25)/(1000(m)))^(mt)


P(t) = 3500 (1+(25)/(1000(12)))^(12t)


P(t) = 3500 (1+(25)/(12000))^(12t)


P(t) = 3500 (1+0.00206)^(12t)


\mathbf{ P(t) = 3500 (1.}00206)^(12t)

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