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,
[tex]\begin{gathered} r=\frac{\text{new amount - previous amount}}{\text{previous amount}} \\ r=\frac{3-1}{1} \\ r=2 \end{gathered}[/tex]where r is expressed as a decimal.
The exponential growth formula is:
[tex]f(t)=a(1+r)^t[/tex]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:
[tex]\begin{gathered} f(t)=35\cdot(1+2)^6 \\ f(t)=35\cdot3^6 \\ f(t)=35\cdot729 \\ f(t)=25515 \end{gathered}[/tex]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
