1 Answer

Pjanssen · Answer 1 · 2023-08-17T09:02:09+0000

Solution:

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

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