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Math Help - Generate range of values exponentially

  1. #1
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    Generate range of values exponentially

    I would like to generate S values from A to B both included, with a logarithmic or exponential increase between the values and I don't know which one could be a good formula to use, right now I'm using:

    m=B/A
    f[1]=A
    f[n+1]=n*(m^{1/S})

    It works well but it doesn't let me control how fast the curve grows, just the start, end and the number of steps. Is there a better one? I thought this would be a fairly used formula but I can't find a straightforward answer anywhere.
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  2. #2
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    Hello, Berem!

    I would like to generate S values from A to B, both included,
    with a logarithmic or exponential increase between the values.
    Here's how I'd approach the log function . . .

    Let: . f(x) \:=\:p\ln(x) + q

    We are given: . \begin{array}{c}f(1) \:=\:A \\ f(5) \:=\:B\end{array}


    Since f(1) = A, we have: . p\ln(1) + q \:=\:A \quad\Rightarrow\quad q \:=\:A

    . . The function (so far) is: . f(x) \;=\;p\ln(x) + A


    Since f(5) = B, we have: . p\ln(5) + A\:=\:B \quad\Rightarrow\quad p \:=\:\frac{B-A}{\ln5}

    . . Therefore, the function is: . f(x) \;=\;\frac{B-A}{\ln5}\,\ln(x) + A

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  3. #3
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    Thanks that logarithmic function works well.

    Is it not possible to get a logarithmic or exponential function where as well as defining the start/end point and the number of values you want to get, you can also modify how fast or slow the curve grows?

    I mean modify the curve from A to B so it generates more values near B or not so near to the point it almost looks like a line.

    Maybe it's not possible to do this with exponentials/logarithmic curves and I should use another kind of curves, any ideas?
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