Question

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

Answer 1

Answer:

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

Step-by-step 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:

$P(t) = 3500 (1+\dfrac{25}{1000})^t$

For monthly growth rate m = 12

$P(t) = 3500 (1+\dfrac{25}{1000(m)})^{mt}$

$P(t) = 3500 (1+\dfrac{25}{1000(12)})^{12t}$

$P(t) = 3500 (1+\dfrac{25}{12000})^{12t}$

$P(t) = 3500 (1+0.00206)^{12t}$

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