Modeling Yeast Growth

Kurt Bryan and SIMIODE

Notebook to support Exercise 2.2.8, modeling yeast population growth.

The data, in time/population pairs:

data = {{0, 9.6}, {1, 18.3}, {2, 29}, {3, 47.2}, {4, 71.1}, {5, 119.1}, {6, 174.6}, {7, 257.3}, {8, 350.7}, {9, 441}, {10, 513.3}, {11, 559.7}, {12, 594.8}, {13, 629.4}, {14, 640.8}, {15, 651.1}, {16, 655.9}, {17, 659.6}}

A plot:

plt1=ListPlot[data,AxesLabel->{"time (hours)","Population (millions)"},PlotStyle->{Red}]

Given that u(0) = 9.6, the solution to the logistic equation with intrinsic growth rate "r" and carrying capacity "K" is

u[t_] = K/(1+Exp[-r*t]*(K/9.6-1))

Take a guess r = 1 and K = 600, plot, compare to the data

plt2 = Plot[u[t]/.{r->1,K->600},{t,0,17},PlotStyle->{Blue}];
Show[plt1,plt2]

Perhaps we can do better...