# Logistic Growth Maplet

This Maplet plots a logistic growth function of the form y(t) = M/(1 + B*exp(-M*k*t)), where M is the carrying capacity, k is the growth constant (if k>0, decay if k<0), and B =(M-y0)/y0, where y0 is the initial amount. y(t) satisfies the differential equation y' = k*y*(M - y). This models restricted growth, where the rate of growth is proportional to the amount times how close the amount is to the carrying capacity of the system.
There are two plotting options. Option 1 lets you directly enter the parameters M, B, and k. Option 2 lets you enter a list of data points, an estimate for M, and then a choice of two data points (eg the 2nd and 5th points), which the Maplet will then use to solve for B and k. The values of M, B, and k appear below the plot. There is a slider to the left of the plot which moves a horizontal line on the plot. This slider may be moved with the mouse or changed incrementally by selecting with the mouse and then using the arrow keys. Enter and plot the data points, then use this slider to approximated the carrying capacity based on the data points. Then enter this value for M (note that moving the slider does NOT change the value for M--this value must be entered manually in the appropriate text box). Finally choose two data points to solve for B and k. Experiment with choices of M, and choices of data points, plotting the function together with all the data points, until you seem to have a good fit.
In Option 2, it is important that the data points be entered as a list of pairs in brackets (the bracketted pairs are the data points), e.g [[0, 1.5], [2, 4.24], [2.8, 9.5]].