Question

The following table gives the percentage, P, of households with a television set that also have a VCR.

Year| 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991
% having VCR| 0.2 0.4 0.7 1.4 2.6 5.1 9.2 15.4 26.3 35.8 45.8 54.6 61.0 64.1

1) If the best fitting logistic function for this data is P= 67/ 1+340e^−0.67t,
(where t is years since 1978) what is the limiting value (as t gets very large)?

2) What is the exact difference (in absolute value), if any, between the value predicted by the given function and the value stated in the table for the year 1991?

Answer 1

#1. e^-t → 0, so
67/(1+340e^(−0.67t)) → 67/(1+340*0) = 67

#2. 67/(1+340e^(−0.67*13)) = 63.44
so, ...