Question:
The fox population in a certain region has a continuous growth rate of 4 percent per year. It is estimated that the population in the year 2000 was 23700.
(a) Find a function that models the population (t) years after 2000 ( t=0 for 2000).
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Answer:
A: P(t)=23700e^(.04t)
B: ≈32638
Explanation:
A: The formula A=Pe^(rt) can be used. Initial value of 23700, e is the exponential constant, the rate is 4% which can be seen as 4/100, and t=time
B: Use the equation you created and substitute 8 for t since the years of difference between 2008-2000 is 8 years
23700e^(.04(8)) ≈ 32637.9280148
Rounded to the nearest fox is ≈32638