The current fox population in a protected region is 367 and is decreasing by 8% per year. Find the exponential function f(x) that represents the fox population, where x is the number of years from now. Estimate the fox population of the region 9 years from now. f (x)=367 x (.97)^x
The exponential function that represents the fox population in the protected region is:
f(x) = 367 * (0.97)^x
To estimate the fox population 9 years from now, we substitute x = 9 into the exponential function:
f(9) = 367 * (0.97)^9
Using a calculator or any software capable of calculating exponentials, we find:
f(9) ≈ 367 * 0.744
f(9) ≈ 273.048
Therefore, the estimated fox population in the region 9 years from now is approximately 273.