Question

a population of fish starts at 8,000 and increases by 6% per year.
what is the fish population in 10 years?

Answer 1

To calculate the fish population after 10 years given an initial population of 8,000 fish that increases by 6% per year, we can use the formula for exponential growth:

\[
P = P_0 \times (1 + r)^t
\]

Where:
- \(P\) is the future population
- \(P_0\) is the initial population (8,000)
- \(r\) is the growth rate (6% or 0.06)
- \(t\) is the time in years (10)

Plugging in the values:

\[
P = 8000 \times (1 + 0.06)^{10}
\]

Calculating \(1 + 0.06\):

\[
1 + 0.06 = 1.06
\]

Now raising it to the power of 10:

\[
1.06^{10} \approx 1.790847
\]

Now we multiply this by the initial population:

\[
P \approx 8000 \times 1.790847 \approx 14326.776
\]

Rounding to the nearest whole number, the fish population after 10 years will be approximately:

\[
\text{Population} \approx 14,327
\]

So, the fish population in 10 years is expected to be about **14,327** fish.