Given:
Annual population of butterflies after t years is
[tex]B(t)=137(1.085)^t[/tex]
To find:
The growth rate.
Solution:
The general exponential function is
[tex]f(t)=a(1+r)^t[/tex] ...(i)
where, a is initial value, t is time and r is growth rate.
We have,
[tex]B(t)=137(1.085)^t[/tex]
It can be written as
[tex]B(t)=137(1+0.085)^t[/tex] ...(ii)
On comparing (i) and (ii), we get
Initial value : [tex]a=137[/tex]
Growth rate : [tex]r=0.085=8.5\%[/tex]
Therefore, the growth rate is 8.5%.
