how long will it take for the population to reach 2128 alligators, according to this model?

From the problem we will have the following:
[tex]\begin{gathered} 2128=(133)4^{t/4}\Rightarrow16=4^{t/4} \\ \\ \Rightarrow ln(16)=ln(4^{t/4})\Rightarrow ln(16)=\frac{t}{4}ln(4) \\ \\ \Rightarrow t=\frac{4ln(6)}{ln(4)}\Rightarrow t\approx5.17 \end{gathered}[/tex]So, the time it will pass will be approximately 5.17 years.