Question

A city has a population of 370,000 people. Suppose that each year the population grows by 3.5% what will the population be after 6 years? Round answer to the nearest whole number

Answer 1

Given that the population is 370000 people.

The growth rate is 3.5% per year.

The number of years =6.

After one year the population is

`=370000+370000*(3.5)/(100)`

`=370000(1+(3.5)/(100))`

`=370000((100+3.5)/(100))`

`=370000((103.5)/(100))`

`=370000*1.035`

After 2 years the population is

`=370000*1.035+370000*1.035*(3.5)/(100)`

`=370000*1.035(1+(3.5)/(100))`

`=370000*1.035*1.035`

`=370000*1.035^2`

Repeating this process, after 6 years, the population is

`=370000*1.035^6`

`=370000*1.229`

`=454730\text{ people.}`

Hence the population after 6 years is 454730 people.