Question

Write a function f(t) that models the number of foxes in the population at t years after 2012…

Answer 1

Write out the continuous growth function formula

`f(t)=Pe^(rt)`

Note that

f(t) is the final value

P= initial value

e=natural number

r= rate

t= time

Write out the given in the question

`\begin{gathered} P=20040 \\ t=t \\ r=(4)/(100)=0.04 \end{gathered}`

Substitute the value of the given into the formula

`f(t)=20040e^(0.04t)`

In the year 2020, the time t would be

`\begin{gathered} t=2020-2012 \\ t=8 \end{gathered}`

Calculate the fox population in 2020

Substitute for t = 8 in the f(t) function

`\begin{gathered} f(t)=20040e^(0,04*8) \\ f(t)=20040e^(0.32) \\ f(t)=27597.6404 \end{gathered}`

Answer Summary

The f(t) gives

`f(t)=20040e^(0.32t)`

The number of foxes in the year 2023 is 27, 598 population