Question

homework assignment 6.1 exponential functions
due sunday by 11:59pm points 12 submitting an external tool
homework assignment 6.1 exponential functions
score: 1/12 answered: 1/12
question 2
the fox population in a certain region has an annual growth rate of 7 percent per year. it is estimated that the population in the year 2000 was 25200.
(a) find a function that models the population t years after 2000 (t = 0 for 2000).
your answer is p(t) =
(b) use the function from part (a) to estimate the fox population in the year 2008.
your answer is (the answer should be an integer)

Explanation:

Step1: Determine the exponential function form

The general form of an exponential growth function is \(P(t)=P_0(1 + r)^t\), where \(P_0\) is the initial population, \(r\) is the growth rate as a decimal, and \(t\) is the number of years. Given \(P_0 = 25200\) and \(r=0.07\), the function is \(P(t)=25200(1 + 0.07)^t=25200(1.07)^t\).

Step2: Calculate the population in 2008

For the year 2008, \(t = 2008 - 2000=8\). Substitute \(t = 8\) into the function \(P(t)=25200(1.07)^t\). So \(P(8)=25200\times(1.07)^8\).
Using a calculator, \((1.07)^8\approx1.718186\). Then \(P(8)=25200\times1.718186\approx43298\).

Answer:

(a) \(P(t)=25200(1.07)^t\)
(b) \(43298\)