Question

How long will it take for the population to reach 6480 alligators according to this model

Answer 1

Given:

`P(t)=(240)3^{(t)/(3)}`

To reach 6480 alligators, this means when P(t) = 6480

`\begin{gathered} 6480=(240)3^{(t)/(3)} \\ (6480)/(240)=3^{(t)/(3)} \\ 27=3^{(t)/(3)} \end{gathered}`

Rewriting the equation in base 3,

`\begin{gathered} 3^3=3^{(t)/(3)} \\ Equating\text{ the exponents,} \\ 3=(t)/(3) \\ Cross\text{ multiplying,} \\ t=3*3 \\ t=9years \end{gathered}`

Therefore, it will take 9 years for the population to reach 6480 alligators