The number of passengers using a railway fell from 190,205 to 174,989 during a 5-year period. Find the annual percentage decrease over this

Question

The number of passengers using a railway fell from 190,205 to 174,989 during a 5-year period. Find the annual percentage decrease over this period.

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2 weeks 2022-01-07T15:35:38+00:00 1 Answer 0 views 0

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  1. Ava
    0
    2022-01-07T15:36:45+00:00

    Answer:

    1.65%

    Step-by-step explanation:

    We will assume the percentage was the same over the 5 years. The number of passengers using a railway is expressed by the formula

                               P(t)  = P_{o}(1 - r)^{t}

    Where

    P(t) is the number of passengers after 5 years

                      P(t) = 174,989

    P₀ is the number of the passengers at the beginning of the period

                     P₀ = 190,205

    r is the rate in percentage    r  = ?

    t is time duration    t = 5 years

    Substituting these given values into the formula,

                     174,989 = 190,205(1 - r)^{5}

                     (1 - r)^{5} = \frac {174,989}{190,205}

                     1 - r = \sqrt[5]{ \frac {174,989}{190,205}}

                     1 - r = \sqrt[5]{0.920}

                     1 - r = 0.9835

                     r = 1 - 0.9835

                     r = 0.0165

                    r = 1.65%

    The annual percentage decrease over the period of 5 years is 1.65%

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