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

and the Gompertz curve

Y = Le^{–be–kt}

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. And in case the last exponent in the Gompertz curve is too small for you to read, it is –kt.) 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 1. Which curve provides the better fit?

Transcribed Image Text:

Y = 1+ ae-bt