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%.