Question

The population of a town increases by 4 % every year . In the last year the population of the town was 110000.

Find the present population of the town .
Find the population of the town in the next year​

Answer 1

114,400 and 118,976.

Explanation:

Let's represent this using a function. Let's let:

`P(y)` represent the total population, and
`y` represent the total number of years since last year.

We know that the population grows by 4% every year or 0.04 every year. This is exponential growth. We can write this as:

`P(y)=110000(1.04)^y`

Note that the coefficient is 110000 because that is the year we are starting with. Also, note that it is 1.04 because we are essentially adding .04 to the original population.

Anyways, to find the present population, set y equal to 1 (because 1 year after last year is the present year)

`P(1)=110000(1.04)^1=114400`

The present population is 114,400 people.

For next year, set y equal to 2 (2 years after last year is next year)>

`P(2)=110000(1.04)^2=118976`

The population next year will be 118,976 people.