Sue owes an amount of £800 Each month, she pays back 20% of the amount she still owes. How much will she still have left to pay

Question

Sue owes an amount of £800
Each month, she pays back 20% of the amount she still owes.
How much will she still have left to pay at the end of five months?

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Thanh Thu 1 month 2021-08-11T09:45:39+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-08-11T09:46:51+00:00

    Answer:

    She will have £262 left to pay at the end of five months.

    Step-by-step explanation:

    Exponential equation for an amount:

    A exponential equation for an amount that decays has the following format:

    A(t) = A(0)(1-r)^{t}

    In which A(0) is the initial amount, r is the decay rate, as a decimal, and t is the time measure.

    Sue owes an amount of £800

    This means that A(0) = 800

    Each month, she pays back 20% of the amount she still owes.

    This means that r = 0.2

    So

    A(t) = A(0)(1-r)^{t}

    A(t) = 800(1-0.2)^{t}

    A(t) = 800(0.8)^{t}

    How much will she still have left to pay at the end of five months?

    This is A(5). So

    A(5) = 800(0.8)^{5} = 262

    She will have £262 left to pay at the end of five months.

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