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Math Help - Growth Factor / Exponential Function

  1. #1
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    Growth Factor / Exponential Function

    So I have this table B, for dollars:

    t: 0, 1, 2, 3
    B: 100, 110, 121, 133.10

    How do i calculate the yearly growth factor for B and find a monthly interest rate?
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  2. #2
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    Quote Originally Posted by MrOoh View Post
    So I have this table B, for dollars:

    t: 0, 1, 2, 3
    B: 100, 110, 121, 133.10

    How do i calculate the yearly growth factor for B and find a monthly interest rate?
    What unit is t measured in?

    And is it simple or compound interest? (I assume from the post title it's compound inteerst, in which case that should have been stated).

    It would help if all of the question was posted rather than just the bits you think are important.

    You will probably need to do an exponential regression to get the growth factor, and compare the value each time period with what the compound interest formula says it should be (treating i as the unknown in each case).
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  3. #3
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    The full question is:

    You deposit 100$ in a savings account. B=B(t) in ollars, t is measured in years

    t;0,1,2,3
    B;100,110,121,133.10

    A) First check if the data is exponential
    I checked by subtracting the B values as follow;
    110 - 100 = 10
    121 - 110 = 11
    133.10 - 121 = 12.10

    Therefore the data is exponential

    These are the 3 questions I am having trouble figuring out:

    B) Find the yearly growth factor for B

    C) Find the exponential function giving the balance B as a function of time t

    D) What monthly interest rate best represents this account?
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  4. #4
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    Quote Originally Posted by MrOoh View Post
    The full question is:

    You deposit 100$ in a savings account. B=B(t) in dollars, t is measured in years

    t;0,1,2,3
    B;100,110,121,133.10

    A) First check if the data is exponential
    I checked by subtracting the B values as follow;
    110 - 100 = 10
    121 - 110 = 11
    133.10 - 121 = 12.10

    Therefore the data is exponential
    How does that tell you that the data is exponential? I would have looked at the quotient of two consecutive values rather than the difference. That also answers "B" for you.

    These are the 3 questions I am having trouble figuring out:

    B) Find the yearly growth factor for B

    C) Find the exponential function giving the balance B as a function of time t

    D) What monthly interest rate best represents this account?
    An "exponential function" can be written as either B(t)= ai^t or B(t)= ae^{rt}. Presumably your teacher or textbook has used one of those (probably the first). You should use the same one. Putting t= 0 and B= 100 into either of those gives you one equation and t= 1, B= 110 gives a second equation. Solve those two equations for a and i (or a and r).

    (That's a pretty good interest rate- I suspect this problem is rather old!)
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  5. #5
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    Ah, so correct me if i'm wrong:

    So since B(t) = ai^t, basically saying the initial value multiplied by the growth factor to the time (t) power and since the common quotient is 1.1, the monthly interest rate would be 1.1 -1 = .1, or 10%.

    So
    B = 100(1.1)^t dollars would be the exponential function for balance B as function of time t in years
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  6. #6
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    Quote Originally Posted by MrOoh View Post
    Ah, so correct me if i'm wrong:

    So since B(t) = ai^t, basically saying the initial value multiplied by the growth factor to the time (t) power and since the common quotient is 1.1, the monthly interest rate would be 1.1 -1 = .1, or 10%.

    So
    B = 100(1.1)^t dollars would be the exponential function for balance B as function of time t in years
    No that would be the annual interest rate.

    CB
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    oh yeah, monthly would just be it divided by 12 so .8% per month
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  8. #8
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    Quote Originally Posted by MrOoh View Post
    oh yeah, monthly would just be it divided by 12 so .8% per month
    You might think that, and it is close. If it had been compounded monthly it would be (1-1.1^{1/12})\times 100 \approx 0.797\%
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