Question

A study of the annual population of butterflies in the country park shows the population,B(t), can be represented by the function B(t)=137(1.085)^t, where the T represents the number of years since the study started based on the function what is the growth rate

Answer 1

Given:

Annual population of butterflies after t years is

`B(t)=137(1.085)^t`

To find:

The growth rate.

Solution:

The general exponential function is

`f(t)=a(1+r)^t` ...(i)

where, a is initial value, t is time and r is growth rate.

We have,

`B(t)=137(1.085)^t`

It can be written as

`B(t)=137(1+0.085)^t` ...(ii)

On comparing (i) and (ii), we get

Initial value :
`a=137`

Growth rate :
`r=0.085=8.5\%`

Therefore, the growth rate is 8.5%.