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Thread: More formula stuff...

  1. #1
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    More formula stuff...

    Ok, so I'm pretty darn sure I'm not setting these up right.

    Saturated growth can be modeled by P(t) = S - Se-kx. Find the exact values of S and k for the graph below if the horizontal asymptote is y = 9 and the indicated point is (1, 7)

    How would I even begin to set this up?
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  2. #2
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    Quote Originally Posted by JAMESveeder View Post
    Ok, so I'm pretty darn sure I'm not setting these up right.

    Saturated growth can be modeled by P(t) = S - Se-kx. Find the exact values of S and k for the graph below if the horizontal asymptote is y = 9 and the indicated point is (1, 7)

    How would I even begin to set this up?
    I think you mean ...

    P(t) = S - Se^{-kt} = S(1 - e^{-kt})

    \lim_{t \to \infty} S(1 - e^{-kt}) = 9 indicates S = 9 since e^{-kt} approaches 0 as t gets large.

    P(1) = 7

    7 = 9(1 - e^{-k})

    solve for k
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