Question

A model predicts that the population of a certain town was 10,000 in 2001. The model also

predicts that each year for the next 5 years, the population p increased by 8% of the previous
year's population. Which equation best represents this model, where X is the number of years after
2001, for X < 5?

Answer 1

The equation that best represents this model is
`P(x) = 10000(1.08)^x`

Explanation:

Exponential equation for population growth:

The exponential equation for population growth, after x years, is given by:

`P(x) = P(0)(1+r)^x`

In which P(0) is the initial population and r is the growth rate.

A model predicts that the population of a certain town was 10,000 in 2001.

This means that
`P(0) = 10000`

8% yearly increase.

This means that
`r = 0.08`. So

`P(x) = P(0)(1+r)^x`

`P(x) = 10000(1+0.08)^x`

`P(x) = 10000(1.08)^x`

The equation that best represents this model is
`P(x) = 10000(1.08)^x`