Question

The function f(x) = 12,000(1 + 0.05)x models the fish population in a lake. What will the population be in 4 years? What was the population 4 years ago?

A. about 12,600; about 11,400
B. about 14,420; about 10,104
C. about 14,586; about 9,872
D. about 56,401; about 6,290

Answer 1

Explanation:

c

Answer 2

C. about 14,586; about 9,872

Explanation:

Given exponential function:

`f(x)=12000(1+0.05)^x`

(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:

`\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}`

To calculate the population 4 years ago, substitute x = -4 into the function:

`\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}`