Answered

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The function [tex]$f(x)=1200(0.8)^x$[/tex] represents the possible elk population of a national park [tex]$x$[/tex] years from now. What is the current population of elk at the park?

A. 1200
B. 960
C. 768
D. 1500

Sagot :

GinnyAnswer
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
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