The given formula is:
[tex]n(t)=66e^{0.015t}[/tex]Where t is measured in years since 2001 and n(t) is measured in millions.
a. What was the rat population in 2001?
Since t is measured in years since 2001, then we need to subtract 2001 from the year we want to analyze. So:
[tex]t=2001-2001=0[/tex]By replacing t=0 into the formula we obtain:
[tex]\begin{gathered} n(0)=66e^{0.015*0} \\ n(0)=66e^0 \\ n(0)=66*1 \\ n(0)=66\text{ millions} \end{gathered}[/tex]As n(t) is measured in millions, thus, the rat population in 2001 was 66000000 rats.
b. What does the model predict the rat population was in the year 2020?
t in the year 2020 is:
[tex]t=2020-2001=19[/tex]Then:
[tex]\begin{gathered} n(19)=66e^{0.015*19} \\ n(19)=66e^{0.285} \\ n(19)=66*1.33 \\ n(19)=87.764294\text{ millions} \end{gathered}[/tex]In the year 2020 the predicted rat population was 87764294 rats.
