To plot this graph, I use second order forward differemce formula for x=0 and second order backward differemce formula for x=40 and second order central difference scheme on the interior.

For d, the delay rate is -1/P * dP/dt and the half life is ln(2)/average delay rate.

Can anyone help me solve this problem? Thanks.

(c) Comment on what you see in the plot of the derivative. You should see something that looks strange/confusing. Why is that? Why isn't it a smooth curve? (d) Based on what you see, why is it a good idea to use the mean of the calculated decay rate to calculate the half life