Question

A wildlife refuge has 200 birds when it is first established. It is so

successful that the number of birds increases by 25% every year.
Write a function to model the situation.
Find the number of birds present after 7 years.

Answer 1

`(a)\ f(x) =200(1.25)^x`

(b) 954 birds after 7 years

Explanation:

Given

`a = 200` --- initial

`r =25\%` --- rate

Solving (a): The function.

This is represented as:

`f(x) =a(1+r)^x`

So, we have:

`f(x) =200(1+25\%)^x`

Express percentage as decimal

`f(x) =200(1+0.25)^x`

`f(x) =200(1.25)^x`

Solving (b): Birds after 7 years

This implies that we calculate f(7)

`f(7) =200(1.25)^7`

`f(7) =953.67`

`f(7) =954` --- approximated