To determine the number of deer in the population 3 years after beginning the study, we can use the function provided by the scientists: [tex]\( f(x) = 248 \times (1.15)^x \)[/tex].
Given:
- [tex]\( x = 3 \)[/tex]
- Initial population [tex]\( P_0 = 248 \)[/tex]
- Growth rate [tex]\( r = 1.15 \)[/tex]
To find the population after 3 years ([tex]\( f(3) \)[/tex]), we substitute [tex]\( x \)[/tex] with 3 in the function:
[tex]\[
f(3) = 248 \times (1.15)^3
\][/tex]
Now, let's break down the calculation step-by-step:
1. Calculate [tex]\( (1.15)^3 \)[/tex]:
[tex]\[
(1.15)^3 = 1.15 \times 1.15 \times 1.15 = 1.15^3 \approx 1.520875
\][/tex]
2. Multiply the result by the initial population:
[tex]\[
248 \times 1.520875 \approx 377.177
\][/tex]
Thus, the population after 3 years is approximately 377.
Among the given options:
- 251
- 377
- 856
- 1,003
The closest answer is 377. Therefore, about 377 deer are in the population 3 years after beginning the study.
