To find the exponential function, we start with the initial value of the fox population, which is 367. Then, we need to consider that the population is decreasing by 8% per year, so the growth rate is -8%. We use this growth rate to form the base of the exponential function.
The exponential decay function is given by:
f(x) = a(1 - r)^x,
where:
f(x) represents the fox population after x years,
a is the initial value of the population,
r is the growth rate expressed as a decimal,
x is the number of years from now.
In this case, a = 367 and r = -8% = -0.08.
Substituting the values into the exponential decay function:
f(x) = 367(1 - 0.08)^x.
To estimate the fox population 9 years from now, we substitute x = 9 into the exponential function:
f(9) = 367(1 - 0.08)^9.
Calculating this expression yields:
f(9) ≈ 183.99.
Therefore, the estimated fox population in the region 9 years from now is approximately 184.
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.
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