To determine the current population of elk at the park, we need to evaluate the function [tex]\( f(x) = 1200(0.8)^x \)[/tex] at [tex]\( x = 0 \)[/tex].
Here’s a detailed step-by-step solution:
1. Identify the function and the given conditions:
The function [tex]\( f(x) = 1200(0.8)^x \)[/tex] represents the elk population [tex]\( x \)[/tex] years from now.
We want to find the population for the current year, which means [tex]\( x = 0 \)[/tex].
2. Substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\[
f(0) = 1200(0.8)^0
\][/tex]
3. Simplify the expression:
Any number raised to the power of 0 is 1. Therefore:
[tex]\[
(0.8)^0 = 1
\][/tex]
4. Multiply the constant term:
[tex]\[
f(0) = 1200 \times 1 = 1200
\][/tex]
Thus, the current population of elk at the park is [tex]\( 1200 \)[/tex].
Therefore, the correct answer is:
C. 1200
