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 per
Question
1 Answer

1. User Answers WaywardDelaney
Answer:
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 .
Stepbystep 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 × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]
Or, The increase population of town after 3 years = p × [tex](1+\dfrac{\textrm 7.5}{100})^{\textrm 3}[/tex]
Or, P = p × [tex](1.075)^{3}[/tex]
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 × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]
Or, The increase population of town after 5 years = p × [tex](1+\dfrac{\textrm 7.5}{100})^{\textrm 5}[/tex]
Or, P' = p × [tex](1.075)^{5}[/tex]
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