The adoption level of a new product often can be modeled as an S-shaped curve called the Pearl (or logistic) curve. The equation of this curve is                          where Y is the adoption...

The adoption level of a new product often can be modeled as an S-shaped curve called the Pearl (or logistic) curve. The equation of this curve is




where Y is the adoption level, L is an (unknown) upper limit on adoptions, and a and b are parameters to be estimated. The file P08_11.xlsx lists information on U.S. cell phones since 1990 (which corresponds to year 1). For this problem, define Y as the number of cell phones per capita. As t increases, Y approaches the limit L. Hence we can use this curve to estimate the upper limit on U.S. cell phones per person. Use Evolutionary Solver to estimate the eventual number of cell phones per person in the United States.