On the day Alexander was born, his father invested $5000in an account with a 1.2% annual growth rate. Write a function, A(t) that represents

Question

On the day Alexander was born, his father invested $5000in an account with a 1.2% annual growth rate. Write a function, A(t) that represents the value of this investment t year after Alexander’s birth. Determine, to the nearest dollar, how much more the investment will be worth when Alexander turns 32 that when he turns 17.
A(t)=Answer
The investment will be worth$ Answer more when alexander turns 32 than when he turns 17

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Sarah 2 weeks 2021-09-12T14:04:26+00:00 1 Answer 0

Answers ( )

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    2021-09-12T14:05:59+00:00

    Answer:

    Equation:  A(t)=5000(1.012)^n

    Worth more in 32 yr than in 17 yr by:  $1199.92

    Step-by-step explanation:

    THe compound growth formula is:

    F=P(1+r)^n

    Where

    F is the future amount (here, A(t))

    P is the initial amount, here 5000

    r is the rate of growth in decimal, 1.2% = 1.2/100 = 0.012

    n is the time in years

    Thus, we can say the function would be:

    A(t)=5000(1+0.012)^n\\A(t)=5000(1.012)^n

    Now, we want how much more it will be worth when 17 years and 32 years. We find the future amount, A(t), when n= 17 and n = 32 and find the difference. Shown below:

    A(t)=5000(1.012)^n\\A(17)=5000(1.012)^{17}\\=6124.05

    and

    A(32)=5000(1.012)^{32}\\=7323.97

    So, it will be worth more by:

    7323.97 – 6124.05 = $1199.92

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