In MATLAB, write a script which

a.) Plots the logisitc curve p=P(t), where , with a title, and axes labeled appropriately.

b.) Plots the derivative q=Q(t), where , with a title, and axes labeled appropriately.

c.) Plots the logit function , with a title, and axes labeled appropriately.

Think how FWHM(Full Width Height Maximum) can be found if we know only the values of a quantity like Q=Q(t), i.e. from the pairs , i=1:N, which are stored in two arrays t and q.

1. Need to find the maximum value of M (height of the peak), and the time it occurs, call it t_peak.

2. Set the cutoff level at half maximum: cut=M/2

3. Find the first time (before t_peak) at which . Call it tLeft.

4. Find the first (after t_peak) at whcih . Call it tRight.

5. Then FWHM=tRight-tLeft.

Plt) = (1 + e-t)