A company introduced a new software product on a trial run in a city. They advertised the product on television and found the following data regarding the percent P of people who bought the product after x ads were run.
Number of Ads, x Percentage Who Bought, P
0 ........................................ 0.2%
10 .......................................... 0.7
20 ......................................... 2.7
30 .......................................... 9.2
40 ........................................ 27.0
50 ........................................ 57.6
60 ........................................ 83.3
70 ........................................ 94.8
80 ........................................ 98.5
90 ........................................ 99.6
a) Use a graphing calculator to fit a logistic function
P(x) = a / (1 + be-kx) to the data.
b) What percent of people bought the product when 55 ads were run 100 ads?
c) Find the horizontal asymptote for the graph. Interpret the asymptote in terms of the advertising situation.