To determine the deer population 3 years after the beginning of the study, we'll use the given function [tex]\( f(x) = 248(1.15)^x \)[/tex] where [tex]\( x \)[/tex] represents the number of years.
1. Identify the known values:
- The initial population of deer, [tex]\( P_0 = 248 \)[/tex].
- The growth rate per year, [tex]\( r = 1.15 \)[/tex].
- The number of years after the beginning of the study, [tex]\( x = 3 \)[/tex].
2. Substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(3) = 248 \times (1.15)^3
\][/tex]
3. Calculate the value of [tex]\( (1.15)^3 \)[/tex]:
- This exponentiation step modifies the growth rate applied over 3 years.
4. Multiply the initial population by the result of the exponentiation:
[tex]\[
f(3) = 248 \times (1.15)^3
\][/tex]
Following these calculations, the number of deer in the population 3 years after the study began is approximately:
[tex]\[
377
\][/tex]
Thus, the correct answer is:
[tex]\[
377
\][/tex]
