To determine the current elk population at the park, we need to evaluate the function [tex]\( f(x) = 1200 \cdot (0.8)^x \)[/tex] at [tex]\( x = 0 \)[/tex]. Here is a detailed, step-by-step solution:
1. Substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\[
f(0) = 1200 \cdot (0.8)^0
\][/tex]
2. Simplify the exponent:
[tex]\[
(0.8)^0
\][/tex]
Any non-zero number raised to the power of 0 is 1. So:
[tex]\[
(0.8)^0 = 1
\][/tex]
3. Multiply the constants:
[tex]\[
f(0) = 1200 \cdot 1 = 1200
\][/tex]
Thus, the current elk population at the park is [tex]\( 1200 \)[/tex]. Therefore, the correct answer is:
A. 1200
