Question

10 The growth of a population of squirrels is given by the equation below where t represents the number of years. G(t) = 250 (1.2)^t (a) What is the initial population of squirrels? (b) By what percentage is the population increasing each year? (c) what will be the population of squirrels after one year?

Answer 1

Exponential growth formula:

`f(t)=a\cdot(1+r)^t`

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

(a) In the equation:

`G(t)=250(1.2)^t`

the initial population of squirrels is 250

(b) the growth rate is 0.2, which means that the population increase by 20% each year

(c) Substituting with t = 1 year, we get:

`\begin{gathered} G(1)=250(1.2)^1 \\ G(1)=250(1.2) \\ G(1)=300 \end{gathered}`

The population will be 300 squirrels