The fox population in a certain region has an annual growth rate of $6 \%$ per year. In the year 2012, there were 22,600 foxes counted in the area. What is the fox population predicted to be in the year 2020? (Round your answer to the nearest whole number.) foxes

Step 1 ：The problem is asking for the fox population in the year 2020, given that the population grows at a rate of 6% per year. This is a compound interest problem, where the principal is the initial population, the rate is the growth rate, and the time is the number of years from 2012 to 2020.

Step 2 ：The formula for compound interest is: \(A = P(1 + \frac{r}{n})^{nt}\) where: \(A\) is the amount of money earned after n years, \(P\) is the principal amount (the initial amount of money), \(r\) is the annual interest rate (in decimal form), \(n\) is the number of times that interest is compounded per year, and \(t\) is the time the money is invested for, in years.

Step 3 ：In this case, the population is compounded annually (\(n=1\)), the initial population (\(P\)) is 22,600, the growth rate (\(r\)) is 6% or 0.06, and the time (\(t\)) is 2020 - 2012 = 8 years.

Step 4 ：So we can substitute these values into the formula to find the fox population in 2020: \(P = 22600\), \(r = 0.06\), \(n = 1\), \(t = 8\)

Step 5 ：Calculate the fox population in 2020: \(A = 36020.96648439704\)

Step 6 ：Round the result to the nearest whole number: \(\text{round}(A) = 36021\)

Step 7 ：Final Answer: The fox population in the year 2020 is predicted to be \(\boxed{36021}\)