Question

A city had a population of 5,175 at the beginning of 1972 and has been growing at 7.1% per year since then. (a) Find the size of the city at the beginning of 2004. A. 19,430 B. 5,607 C. 6,275 D. 4,910

Answer 1

The size of the city at the beginning of 2004 is 46,470 to the nearest whole number.

What is the size of the city at the beginning of 2004?

Population at the beginning of 1972 = 5,175

Population growth rate = 7.1%

Population at the beginning of 2004

Number of years = 32 years

`x_(t) = x_(0) * {(1 + r)}^(t)`

`x_(t) = 5175 * {(1 + 0.071)}^(32)`

`x_(t) = 5175 * {(1.071)}^(32)`

`x_(t) = 5175 * 8.979725616`

`x_(t) = 46470.08`

Therefore, the population is 46,470 at the beginning of 2004.