We have the exponential function [tex]f(t)=500(0.78)^t[/tex] for the population of an ant colony.
Since the base (0.78) is less than one, the population is decaying at a rate of: [tex]rate=(1-0.78)[/tex]*100%=22% each month.
Lets find the value of our function at [tex]t=0[/tex]
[tex]f(t)=500(0.78)^t[/tex]
[tex]f(0)=500(0.78)^0[/tex]
[tex]f(0)=500(1)[/tex]
[tex]f(0)=500[/tex]
We can conclude that the correct interpretation of the function at [tex]t=0[/tex] is that the initial population of the ant colony is 500.
