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Science Forum Index » Mathematics Forum » Integral of a logistic equation
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| Euh |
 Posted: Tue Apr 29, 2008 11:09 am |
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Assuming the following general logisitic equation:
y = A/(exp(B*t)+C*exp(-D*t))
This equation describes the exponential growth and decay of variable
"y" with time.
Is it possible to get an expression for the integral of y with respect
to t ? (or a good approximation) |
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| William Elliot |
| Posted: Tue Apr 29, 2008 10:58 pm |
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On Tue, 29 Apr 2008, Euh wrote:
Quote: Assuming the following general logisitic equation:
y = A/(exp(B*t)+C*exp(-D*t))
integral y dt =
-a/b * e^(-bt) - c/d * e^(-dt),
assuming bd /= 0.
Quote: This equation describes the exponential growth and decay of variable
"y" with time.
Is it possible to get an expression for the integral of y with respect
to t ? (or a good approximation)
May I suggest you get a better background in math for your field. |
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| David W. Cantrell |
| Posted: Tue Apr 29, 2008 11:56 pm |
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William Elliot <marsh@hevanet.remove.com> wrote:
Quote: On Tue, 29 Apr 2008, Euh wrote:
Assuming the following general logisitic equation:
y = A/(exp(B*t)+C*exp(-D*t))
integral y dt =
-a/b * e^(-bt) - c/d * e^(-dt),
assuming bd /= 0.
No, William. You seem to have misread the function to be integrated.
Quote: This equation describes the exponential growth and decay of variable
"y" with time.
Is it possible to get an expression for the integral of y with respect
to t ? (or a good approximation)
May I suggest you get a better background in math for your field.
Euh: Please ignore William's remark above.
Perhaps this result from Mathematica will be helpful:
Integrate[a/(Exp[b*t] + c*Exp[-d*t]), t] is
a/(c*d) * E^(d*t) *
Hypergeometric2F1[1, d/(b + d), (b + 2*d)/(b + d), -(E^((b + d)*t)/c)]
David |
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| William Elliot |
| Posted: Wed Apr 30, 2008 12:07 am |
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On Tue, 30 Apr 2008, David W. Cantrell wrote:
Quote: William Elliot <marsh@hevanet.remove.com> wrote:
On Tue, 29 Apr 2008, Euh wrote:
Assuming the following general logisitic equation:
y = A/(exp(B*t)+C*exp(-D*t))
integral y dt =
-a/b * e^(-bt) - c/d * e^(-dt),
assuming bd /= 0.
No, William. You seem to have misread the function to be integrated.
y = A/(exp(B*t) + C*exp(-D*t))
Shucks, did it again. |
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