Question

A city with a population of 28,405 people is predicted to grow exponentially, at an annual rate of 2.4% which of the following equations should be should be used to find the population of the city 5 years from now?

A.p(5)=28,405(1+0.024)^5
B.p(5)=28,405(1-0.024)^5
C.p(5)=28,405(1+5)^2.4
D.p(5)=28,405(1+0.24)^5

Answer 1

The population of city after 5 years is 28,405
`(1+0.024)^(\textrm 5)` .

Explanation:

Given as :

The initial population of city = p = 28,405

The rate of grow of population = r = 2.4% annual

The time period for population = t = 5 years

Let The population of city after 5 years = P

Now, According to question

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

Or, The Population of city after 5 years = initial population ×
`(1+(\textrm rate)/(100))^(\textrm time)`

Or, P = p ×
`(1+(\textrm r)/(100))^(\textrm t)`

Or, P = 28,405 ×
`(1+(\textrm 2.4)/(100))^(\textrm 5)`

Or, P = 28,405 ×
`(1+0.024)^(\textrm 5)`

So, The population of city after 5 years = P = 28,405
`(1+0.024)^(\textrm 5)`

Hence, The population of city after 5 years is 28,405
`(1+0.024)^(\textrm 5)` . Answer