Question

P=130t+17800 gives the total population, P, of a small city t years after 1951. Use the equation to determine when (what year) the population reached a population of 19880 people.

The population reached a total of 19880 people in what year?

Answer 1

The population reached a total of 19880 people in 1967.

Explanation:

The population in t years after 1951 is given by:

`P(t) = 130t + 17800`

Which year the population reached a population of 19880 people.

This is t years after 1951

t is found when
`P(t) = 19880`

So

`P(t) = 130t + 17800`

`19880 = 130t + 17800`

`130t = 2080`

`t = (2080)/(130)`

`t = 16`

1951 + 16 = 1967

The population reached a total of 19880 people in 1967.