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  

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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 a new device. Use Evolutionary Solver to fit a Pearl and a Gompertz curve to these data. Let t  0 correspond to year