Answer:
a) [tex]P(t) = 17900e^{0.04t}[/tex]
b) The population estimated in 2008 is of 24651.
Step-by-step explanation:
The population growth model may be given by the following exponential function:
[tex]P(t) = P_{0}e^{rt}[/tex]
In which P(t) is the population after t years, [tex]P_{0}[/tex] is the initial population and r is the growth rate.
(A.) Find a function that models the population t years after 2000 (t=0 for 2000)
We have that:
[tex]P_{0} = 17900, r = 0.04[/tex]. So
[tex]P(t) = P_{0}e^{rt}[/tex]
[tex]P(t) = 17900e^{0.04t}[/tex]
(B.) Use the function from part A to estimate the fox population in the year 2008.
2008 is 8 years after 2000. So:
[tex]P(8) = 17900e^{0.04*8} = 24650.5[/tex]
The population estimated in 2008 is of 24651.
