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Thread: Functions with points

  1. #1
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    Functions with points

    Find the function f(t) = ce^(kt)
    A) (2,4) and (3,7)

    Now is there anyone out there that can take this step by step please. I want to arrive at the answer with you.THANKS
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  2. #2
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    $\displaystyle f(t) = Ce^{kt}$

    you know $\displaystyle f(2) = 4$ ...

    $\displaystyle 4 = Ce^{k \cdot 2} = C e ^{2k}$

    you also know $\displaystyle f(3) = 7$ ...

    $\displaystyle 7 = Ce^{k \cdot 3} = C e^{3k}$

    set up a ratio using the two equations ...

    $\displaystyle \frac{C e^{3k}}{C e ^{2k}} = \frac{7}{4}$

    doing the division, note that C divides out to be 1, and the division on the left side simplifies to ...

    $\displaystyle e^k = \frac{7}{4}$

    natural log both sides ...

    $\displaystyle k = \ln\left(\frac{7}{4}\right)$

    you now have k ... go back to either of the first equations and solve for C.

    $\displaystyle Ce^{2k} = 4$

    $\displaystyle C(e^k)^2 = 4$

    $\displaystyle C\left(\frac{7}{4}\right)^2 = 4$

    $\displaystyle C = \frac{4^3}{7^2}
    $
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  3. #3
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    so it would be y = 64/49*e^(ln7/4)t as the answer
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