In 2002, there were 972 students enrolled at Oakview High School. Since then, the number of students has increased by 1.5% each year. Write

Question

In 2002, there were 972 students enrolled at Oakview High School. Since then, the number of students has increased by 1.5% each year. Write an exponential function to model the situation, then find the number of students enrolled in 2014. Is this considered growth or decay?

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Natalia 1 month 2021-10-22T09:56:37+00:00 1 Answer 0 views 0

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    2021-10-22T09:57:53+00:00

    Answer:

    N(t) = 972(1.015)^{t}

    Growth function.

    The number of students enrolled in 2014 is 1162.

    Step-by-step explanation:

    The number of students in the school in t years after 2002 can be modeled by the following function:

    N(t) = N(0)(1+r)^{t}

    In which N(0) is the number of students in 2002 and r is the rate of change.

    If 1+r>1, the function is a growth function.

    If 1-r<1, the function is a decay function.

    In 2002, there were 972 students enrolled at Oakview High School.

    This means that N(0) = 972

    Since then, the number of students has increased by 1.5% each year.

    Increase, so r is positive. This means that r = 0.015

    Then

    N(t) = N(0)(1+r)^{t}

    N(t) = 972(1+0.015)^{t}

    N(t) = 972(1.015)^{t}

    Growth function.

    Find the number of students enrolled in 2014.

    2014 is 2014-2002 = 12 years after 2002, so this is N(12).

    N(t) = 972(1.015)^{t}

    N(12) = 972(1.015)^{12}

    N(12) = 1162

    The number of students enrolled in 2014 is 1162.

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