Question

A population of 2000 fish increases at an annual rate of 7.5%. Write the model, then predict how

Answer 1

Answer:

The model is $P(t) = 2000(1.075)^{t}$.

There will be 4122 fish in 10 years.

Step-by-step explanation:

Exponentially increasing population:

An exponentially increasing population can be represented by the following model:

$P(t) = P(0)(1+r)^t$

In which P(t) is the population after t years, P(0) is the initial population, and r is the growth rate, as a decimal.

A population of 2000 fish increases at an annual rate of 7.5%.

This means that $P(0) = 2000, r = 0.075$

So

$P(t) = P(0)(1+r)^t$

$P(t) = 2000(1+0.075)^t$

$P(t) = 2000(1.075)^{t}$

This is the model.

How many fish will there be in 10 years?

This is P(10).

$P(t) = 2000(1.075)^{t}$

$P(10) = 2000(1.075)^{10} = 4122$

There will be 4122 fish in 10 years.