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 9 years from now.
f(x)= 367
* Response area The estimated fox population 9 years from now will be Response area
To find the exponential function F(x) that represents the fox population, we can use the formula:
F(x) = P(1 - r)^x
Where:
F(x) is the fox population after x years
P is the initial population (367)
r is the rate of decrease as a decimal (8% = 0.08)
x is the number of years from now
Substituting the given values into the formula, we get:
F(x) = 367(1 - 0.08)^x
To estimate the fox population 9 years from now, we substitute x = 9 into the function:
F(9) = 367(1 - 0.08)^9
Calculating this expression:
F(9) ≈ 367(0.92)^9
≈ 367(0.471)
≈ 172.577
Therefore, the estimated fox population 9 years from now is approximately 172.577.