Question

A little towns population is growing at an annual rate of 7.5%, annually. What is it’s growth rate per 3 years? Per 5 years? Round to the nearest tenth of a percent.

Answer 1

A) The increase population of town after 3 years is 1.2 times initial population

B) The increase population of town after 5 years is 1.4 times initial population .

Explanation:

Given as :

The rate of growth of population of a town = r = 7.5%

Let The initial population of town = p

A ) Let The increase population of town after 3 years = P

The time period = n = 3 years

Now, According to question

The increase population of town after n years = initial population of town ×
`(1+(\textrm rate)/(100))^(\textrm time)`

Or, The increase population of town after n years = initial population of town ×
`(1+(\textrm r)/(100))^(\textrm n)`

Or, The increase population of town after 3 years = p ×
`(1+(\textrm 7.5)/(100))^(\textrm 3)`

Or, P = p ×
`(1.075)^(3)`

Or, P = p × 1.242

So, The increase population of town after 3 years = P = 1.2 times initial population

Hence,The increase population of town after 3 years is 1.2 times initial population . Answer

B ) Let The increase population of town after 5 years = P'

The time period = n = 5 years

Now, According to question

The increase population of town after n years = initial population of town ×
`(1+(\textrm rate)/(100))^(\textrm time)`

Or, The increase population of town after n years = initial population of town ×
`(1+(\textrm r)/(100))^(\textrm n)`

Or, The increase population of town after 5 years = p ×
`(1+(\textrm 7.5)/(100))^(\textrm 5)`

Or, P' = p ×
`(1.075)^(5)`

Or, P' = p × 1.4356

So, The increase population of town after 5 years = P' = 1.4 times initial population

Hence,The increase population of town after 5 years is 1.4 times initial population . Answer