[tex]P(t)=(674)3^{\frac{t}{2}}[/tex]
To find the tripling time, you have to calculate the time when the population will triple.
First, calculate the initial population of the animal by substituting t=0 into the function:
[tex]P(0)=(674)3^{\frac{0}{2}}=(674)3^0=674\times1=674[/tex]
It follows that the population triples when P(t)=674×3=2022.
Substitute this value into the function and solve for t:
[tex]\begin{gathered} 2022=(674)3^{\frac{t}{2}} \\ \Rightarrow3^{\frac{t}{2}}=\frac{2022}{674}\Rightarrow3^{\frac{t}{2}}=3 \\ \Rightarrow3^{\frac{t}{2}}=3^1\Rightarrow\frac{t}{2}=1 \\ \Rightarrow t=2\times1=2 \end{gathered}[/tex]
Hence, the tripling time is 2 years.
