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i know the values of μ_max, Y, Ks , the initial S (S(0)) the final S and the time Tb that I want to find the specific final S, how can I find the Xa????
Can I use Runge Kutta?

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Alan Stevens
Alan Stevens 2021-1-12

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Your equation has the following analytic solution (assuming Xa is a constant):
You can plug in the known values for S0 (ie. the value of S at time t=0) and the values for t = tend and S at t=tend, then rearrange to get Xa.

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