The adoption level of a new product can often be modeled as an S-shaped curve called the

Question:

The adoption level of a new product can often 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, t is time (in years), 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 t =1). For this problem, define Y as the number of cell phones per capita. As t increases, Y approaches the limit L. Therefore, you 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.