(a) For the U.S. census data, use the forward difference approximation to the deriva...

(a) For the U.S. census data, use the forward difference approximation to the derivative, that is,

to recompute column 5 of Table 3.1.

(b) Using the data from part (a), determine the constants A, p1 in the least-squares fit

(c) With the values for A and p1 found in part (b), determine p0 by averaging formula (21) over the data.

(d) Substitute A, p1, and p0 as determined above into the logistic formula (15) and calculate the populations predicted for each of the years listed in Table 3.1.

(e) Compare this model with that of the centered difference-based model in column 6 of Table 3.1.