To determine the deer population 3 years after the beginning of the study, let's use the given function:
[tex]\[ f(x) = 248(1.15)^x \][/tex]
where \( x \) represents the number of years. In this case, we are interested in the population after 3 years, so we substitute \( x = 3 \) into the function:
1. Substitute \( x = 3 \) into the function:
[tex]\[ f(3) = 248(1.15)^3 \][/tex]
2. Calculate the term \( (1.15)^3 \):
[tex]\[ (1.15)^3 \approx 1.520875 \][/tex]
3. Then multiply this result by the initial population count of 248:
[tex]\[ 248 \times 1.520875 \approx 377.177 \][/tex]
So, approximately 3 years after beginning the study, the deer population is about 377.
Therefore, the correct answer is:
[tex]\[ \boxed{377} \][/tex]
