MTH 306 Spring 2016 MAPLE LAB 2 This investigation deals with the problem of tting a logistic model to given population data. Thus we want to determine the numerical constants a and b so that the solution P (t) of the initial value problem dP = aP + bP 2 , dt P (0) = P0 approximates the given values P0 , P1 , ..., Pn of the population at the times t0 = 0, t1 , ..., tn . If we rewrite the above ODE (the logistic equation with kM = a and k = b) in the form 1 dP = a + bP P dt then we see that the points (P (ti ), P (ti )/P (ti )), i = 1, ..., n, should all lie on the straight line with y-intercept a and slope b. We use the following symmetric dierence approximation to generate P (ti ) Pi+1 Pi1 ti+1 ti1 for the world population (in billions) data given in gure 2.1.11 on page 86 of your textbook. Here we take t = 0 to be 1960, and P0 = 3.049. MTH 306 Spring 2016 Investigation: Use the above symmetric dierence approximation to nd the slope data, P (ti ), for gure 2.1.11 on page 86 of the text. For example, P1 = 3.721 3.049 . 10 Next, use this information to plot the data points (Pi , Pi /Pi ). Your data plot should have a title. Then use your data points to estimate the parameters a and b that give the line of \"best t\