Question

A breeding group of beavers is introduced into a protected area. After t years the number of beavers in the area is modeled by the function

N(t)= 54/0.35+0.68^t

1. How many beavers were initially introduced?
2. Estimate the number of beavers after 5 years.
3. Determine the change in the beaver population between t = 5 and t = 10.

(Note: All answers are whole numbers.)

Answer 1

`N(t)=(54)/(0.35+0.68^t)`

The number of beavers initially introduced is the population at time
`t=0`, so you need to find
`N(0)`.


`N(0)=(54)/(0.35+0.68^0)=(54)/(1.35)=40`

The number of beavers after 5 years is given by
`N(5)`.


`N(5)=(54)/(0.35+0.68^5)\approx(54)/(0.495)\approx109`

The change in the beaver population between
`t=5` and
`t=10` is simply the difference
`N(10)-N(5)`. Evaluate the function at these points (you already know
`N(5)`) and subtract. You should get approximately
`36.49\approx36`.