Peter has saved $10. He doubles the amount he saves each week. Does this represent a exponential function? If so, please write down the func

Question

Peter has saved $10. He doubles the amount he saves each week. Does this represent a exponential function? If so, please write down the function.

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Camila 2 weeks 2021-10-14T00:38:54+00:00 1 Answer 0

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    2021-10-14T00:40:37+00:00

    Answer:

    y=10(2)^x

    Step-by-step explanation:

    This is an exponential function.  Peter is not simply adding $10 a week to his savings, he’s doubling each value each week.  The first case of adding $10 a week is linear.  

    The standard form of an exponential equation is

    y=a(b)^x

    where a is the initial amount and b is the growth or decay factor.  We know a = 10 because we are told he started with $10.  After the first week he would have $20 then because $10 doubled is $20.  That coordinate is (1, 20).  We will use that in place of x and y and solve for b:

    20=10(b)^1

    b to the first is just b, so what we have essentially is 10b = 20, so b = 2.  The equation then is:

    y=10(2)^x

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