Mathematics

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.

1 Answer

  • 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 .

    Step-by-step 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

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