Answer:
5 years
Step-by-step explanation:
If the population of penguins is given by the function:
[tex]P(t)=P_0\cdot 3^{t/5}[/tex]
Initial Size =[tex]P_0[/tex]
Triple its Initial Size, P(t)=[tex]3P_0[/tex]
Therefore:
[tex]3P_0=P_0\cdot 3^{t/5}\\$Divide both sides by P_0\\3=3^{t/5}\\$Since they have the same base\\1=t/5\\Cross multiply\\t=5[/tex]
It therefore takes 5 years for the penguin population to triple in size.
