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Math Help - exponential function

  1. #1
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    exponential function

    A person invests $7000 at 10% interest compounded annually. Let f(t) be the value (in dollars) of the account at t years after he/she has deposited the $7000.

    a. Find an equation of f.

    My answer: f(t)=7000(1.10)^t

    b. What is the base b of your model f(t)=ab^t? What does it mean in this situation?

    My answer: 1.10; the account balance increases by 10% each year.

    c. What is the coefficient a of f(t)=ab^t? What does it mean in this situation?

    My answer: 7000; the initial amount invested was $7000.

    d. What will be the account's value in 10 years? Explain why the value has more than doubled, even though the investment earned 10% for 10 years.

    My answer: For the first part I got $18156. But what would be the explanation? That I don't get...
    Last edited by mt_lapin; March 12th 2008 at 06:27 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by mt_lapin View Post
    A person invests $7000 at 10% interest compounded annually. Let f(t) be the value (in dollars) of the account at t years after he/she has deposited the $7000.

    a. Find an equation of f.

    My answer: f(t)=7000(1.10)^t

    b. What is the base b of your model f(t)=ab^t? What does it mean in this situation?

    My answer: 1.10; the account balance increases by 10% each year.

    c. What is the coefficient a of f(t)=ab^t? What does it mean in this situation?

    My answer: 7000; the initial amount invested was $7000.

    d. What will be the account's value in 10 years? Explain why the value has more than doubled, even though the investment earned 10% for 10 years.

    My answer: For the first part I got $18156. But what would be the explanation? That I don't get...
    Because the balance is compounded annualy you are earning interest on the interest paid in earlier years. So while the interest on the original sum over 10 years is $7000 the account balance has more than doubled because of this interest on interest.

    RonL
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