Sales of a product over time often follow an S-shaped curve. Two functions that yield S-shaped curves are the Pearl (or logistic) curve Y  

1

L aebt 

and the Gompertz curve Y  Lebekt Here, Y is annual sales, t is time (in years), L is the upper limit on sales, and

a, b, and k are parameters to be estimated. (Actually, L must also be estimated.) The file P08_12.xlsx contains data for sales of answering machines in the United States. Use the Evolutionary Solver to fit a Pearl and a Gompertz curve to these data. Let t  0 correspond to 1983. Which curve provides the better fit? (Hint: You need to use reasonable bounds for the parameters for each curve. For example, L  14.5 is reasonable.)