Answer :
Ok, so
Here we have the function:
[tex]P(t)=944(3)^{\frac{t}{3}}[/tex]Now we want to find the tripling-time for this population of deer.
If we make t=0, we will find the initial population of deer. This is:
[tex]P(0)=944(3)^{\frac{0}{3}}=944[/tex]Now, we want to find the time "t" such that this population is the triple.
This is:
[tex]\begin{gathered} 944(3)=944(3)^{\frac{t}{3}} \\ 2832=944(3)^{\frac{t}{3}} \\ \frac{2832}{944}=3^{\frac{t}{3}} \\ 3=3^{\frac{t}{3}} \end{gathered}[/tex]We got this exponential equation:
[tex]3=3^{\frac{t}{3}}[/tex]As the base is the same, we could equal the exponents:
[tex]\begin{gathered} 1=\frac{t}{3} \\ t=3 \end{gathered}[/tex]Therefore, tripling-time for this population of deer are 3 years.