# Limited Growth Maplet

This Maplet plots a limited growth function of the form y(t) = M*(1 - exp(-k*t)), where M is the carrying capacity, and k is the growth constant. It satisfies the differential equation y' = k*(M - y). This models unrestricted growth, where the rate of growth is proportional to how close the amount is to the carrying capacity of the system.
There are two plotting options. Option 1 lets you directly enter the carrying capacity, M, and the growth constant k. Option 2 lets you enter a list of data points, an estimate for M, and then choose one of the points (eg the 2nd point), which the Maplet will then use to solve for k. The values of M 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 in the appropriate text box). Finally chose a representative data point to solve for k. Experiment with choices of M and 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 bracketed pairs are the data points), e.g [[0, 1.5], [2, 4.24], [2.8, 9.5]].
The two check boxes under the plot toggle the function and data points on and off. This only works if Option 2 is selected.