Question

The town of madison has a population of 25,000. The population is increasing by a factor of 1.12 each year. Write a function that gives the population P(t) in madison t years from now

Answer 1

The population P(t) at the end of year t is
`P(t) = 25,000 * (1.12)^t`

Explanation:

The initial population of town of Madison = 25,000

The rate at which the population is increasing = 1.12 times

So, the increase in population first year :

( the initial population) x
`(1.12)^1` = 1.12 x ( 25,000)

= 28,000

So, the population at the end of first year = 28,000

Similarly, the increase in population second year :

( the initial population) x (1.12)² = ( 25,000) x (1.12)²

= 31,360

So, the population at the end of second year =31,360

Now, to calculate the population in t years from now:

The population P(t) at the end of year t is

`P(t) = 25,000 * (1.12)^t`