(a) The point of diminishing returns (i.e., the inflection point) appears to take place during the year 1987.
(b) The best-fitting logistic function for this data is:
P = 61 / (1 + 300 * e^-0.67t)
The limiting value (as t gets very large) is 61%.
(c) For the year 1989, the value stated in the table is 53.4%. To find the value predicted by the given function, we need to plug in the value of t (years since 1978) into the function:
t = 1989 - 1978 = 11
P = 61 / (1 + 300 * e^(-0.67 * 11))
P ≈ 65.4%
The exact difference (in absolute value) between the value predicted by the given function and the value stated in the table for the year 1989 is:
|65.4 - 53.4| = 12%
The following table gives the percentage, P, of households with a television set that also have a VCR. (Unlike the data in your textbook, this data is fictícious).
Year 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 % having VCR 0.2 0.4 0.7 1.5 2.8 5.2 9.7 16.6 24.5 36.1 44,5 53.4 55.6 57.0
(a) During what year does the point of diminishing returns (.e., the inflection point) appear to take place?
During the year
1987
(b) of the best fitting logistic function for this data is
P=
61
1+300e 0.67
(where is years since 1978) what is the limiting value (as t gets very large)?
83
percent
(c) 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 1989? 12
1 answer
1 answer