Question

In the year 2019, Lee County used approximately 55 million gallons of water. Historical trends show that each year the water demand is increasing by a rate of approximately 2.1%. If this trend continues, approximately how many million gallons of water will be used by Lee County by the year 2025? Round to the nearest million

Answer 1

Approximately 62 gallons of water will be used by Lee County by the year 2025.

Explanation:

The amount, in millions gallons of water, spent by Lee County, in t years after 2019, is given by the following equation:

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

In which P(0) is the amount spent on 2019 and r is the increse rate, as a decimal.

In the year 2019, Lee County used approximately 55 million gallons of water.

This means that
`P(0) = 55`

Historical trends show that each year the water demand is increasing by a rate of approximately 2.1%.

This means that
`r = 0.021`

So

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

`P(t) = 55(1 + 0.021)^(t)`

`P(t) = 55(1.021)^(t)`

Approximately how many million gallons of water will be used by Lee County by the year 2025?

2025 is 2025 - 2019 = 6 years after 2019. So this is P(6).

`P(t) = 55(1.021)^(t)`

`P(6) = 55(1.021)^(6)`

`P(6) = 62.3`

Rounded to the nearest millions

Approximately 62 gallons of water will be used by Lee County by the year 2025.