Question

The local rabbit population triples every month. If there are currently 35 rabbits, how many rabbits will there be in 6 months?

Answer 1

First, we need to calculate the growth rate (r). Given that the population triples every month, then if in one month you have 1 rabbit, in the next month you will have 3 rabbits. That is,

`\begin{gathered} r=\frac{\text{new amount - previous amount}}{\text{previous amount}} \\ r=(3-1)/(1) \\ r=2 \end{gathered}`

where r is expressed as a decimal.

The exponential growth formula is:

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

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

Substituting with a = 35, r = 2, and t = 6, we get:

`\begin{gathered} f(t)=35\cdot(1+2)^6 \\ f(t)=35\cdot3^6 \\ f(t)=35\cdot729 \\ f(t)=25515 \end{gathered}`

There will be 25515 rabbits in 6 months

Notice that rate, r, was computed considering two consecutive months because time, t, is measured in months