Construct exponential functiom of points (0,200) and (6,380).

The exponential function is

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  1. let the exponential equation be y = a e^(kx)
    for (0,200)
    200 = a e^0
    a = 200

    so you have y = 200 e^kx
    for (6,380)
    380 = 200 e^(6k)
    1.9 = e^(6k)
    take ln of both sides, and use rules of logs
    ln 1.9 = 6k lne, but lne = 1
    6k = ln 1.9
    k = ln 1.9/6

    the exponential equation is
    y = 200 e^(ln1.9/6 x)

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