The crime rate of a certain city is increasing by exactly 2 % 2 % each year. If there were 450 450 crimes in the year 1990 and the crime

Question

The crime rate of a certain city is increasing by exactly 2 % 2 % each year. If there were 450 450 crimes in the year 1990 and the crime rate remains constant each year, determine the approximate number of crimes in the year 2017 2017 .

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Ximena 8 months 2021-10-04T03:27:26+00:00 1 Answer 0 views 0

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    2021-10-04T03:28:44+00:00

    Answer:

    768 crimes

    Step-by-step explanation:

    we know that

    The equation of a exponential growth function is equal to

    [tex]y=a(1+r)^x[/tex]

    where

    y —-> is the number of crimes

    x —-> ┬áis the number of years since 1990

    r is the rate of chance

    a is the initial value

    we have

    [tex]a=450\ crimes\\r=2\%=2/100=0.02[/tex]

    substitute

    [tex]y=450(1+0.02)^x[/tex]

    [tex]y=450(1.02)^x[/tex]

    Determine the approximate number of crimes in the year 2017

    Find the value of x

    [tex]x=2017-1990=27\ years[/tex]

    substitute the value of x

    [tex]y=450(1.02)^{27}=768\ crimes[/tex]

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