Question

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.(1 point)
Responses

f
(
x
)
=
367
⋅
0.98
x
The estimated fox population 9 years from now will be 306.
f of x is equal to 367 times 0 point 9 8 to the x th power The estimated fox population 9 years from now will be 306.

f
(
x
)
=
367
⋅
1.08
x
The estimated fox population 9 years from now will be 734.
f of x is equal to 367 times 1 point 0 8 to the x th power The estimated fox population 9 years from now will be 734.

f
(
x
)
=
367
⋅
0.92
x
The estimated fox population 9 years from now will be 3,039.
f of x is equal to 367 times 0 point 9 2 x The estimated fox population 9 years from now will be 3,039.

f
(
x
)
=
367
⋅
0.92
x
The estimated fox population 9 years from now will be 173.

Answer 1

Decrease by 8% → decay factor = 1 − 0.08 = 0.92.

f(x) = 367(0.92)^x.

f(9) = 367(0.92)^9 ≈ 367(0.471458) ≈ 173.0, so about 173 foxes (rounded to the nearest whole fox).