Solution:
Given:
[tex]P(t)=(240)3^{\frac{t}{3}}[/tex]
To reach 6480 alligators, this means when P(t) = 6480
[tex]\begin{gathered} 6480=(240)3^{\frac{t}{3}} \\ \frac{6480}{240}=3^{\frac{t}{3}} \\ 27=3^{\frac{t}{3}} \end{gathered}[/tex]
Rewriting the equation in base 3,
[tex]\begin{gathered} 3^3=3^{\frac{t}{3}} \\ Equating\text{ the exponents,} \\ 3=\frac{t}{3} \\ Cross\text{ multiplying,} \\ t=3\times3 \\ t=9years \end{gathered}[/tex]
Therefore, it will take 9 years for the population to reach 6480 alligators
