Question

The fox population in a certain region has an annual growth rate of 5 percent per year. It is estimated that the population in the year 2020 was 20600. (a) Find a function that models the population t years after 2020 (t=0 for 2020). Your answer is P(t)= (b) Use the function from part (a) to estimate the fox population in the year 2028. Your answer is (the answer should be an integer)

Answer 1

a)

`P(t)=20600(1.05)^t`

b) 30436

Step-by-step explanation:

An exponential growth function is usually given as;

`P(t)=a(1+r)^t`

where a = initial amount = 20600

r = rate of increase in decimal = 5% = 5/100 = 0.05

t = time in years

a) So a function that models the population t years after 2020 can be written as;

`\begin{gathered} P(t)=20600(1+0.05)^t \\ P(t)=20600(1.05)^t \end{gathered}`

b) In the year 2028, t = 8, let's go ahead and solve for P(8);

`P(8)=20600(1.05)^8=20600(1.47745544379)=30436`

So in the year 2028, the population will be 30436