Answer:
C. about 14,586; about 9,872
Step-by-step explanation:
Given exponential function:
[tex]f(x)=12000(1+0.05)^x[/tex]
(where f(x) is the population of fish in a lake and x is the number of years).
To calculate the population in 4 years time, substitute x = 4 into the function:
[tex]\begin{aligned}x=4 \implies f(4)&=12000(1+0.05)^4\\&=12000(1.05)^4\\&=12000(1.21550625)\\&=14586.075\\ & \approx 14586\end{aligned}[/tex]
To calculate the population 4 years ago, substitute x = -4 into the function:
[tex]\begin{aligned}x=-4 \implies f(4)&=12000(1+0.05)^{-4}\\&=12000(1.05)^{-4}\\&=12000(0.8227024748)\\&=9872.429698\\ & \approx 9872 \end{aligned}[/tex]
