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 ficticious). Year 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 % having VCR 0.2 0.4 0.8 1.5 3.0 5.1 9.8 17.2 27.9 38.3 48.2 56.8 59.7 62.1 (a) During what year does the point of "diminishing returns" (i.e., the inflection point) appear to take place? During the year ________________ (b) If the best fitting logistic function for this data is P=(69)/(1+340e−0.67t) (where t is years since 1978) what is the limiting value (as t gets very large)? _____________________ 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 1985?
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 ficticious). Year 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 % having VCR 0.2 0.4 0.8 1.5 3.0 5.1 9.8 17.2 27.9 38.3 48.2 56.8 59.7 62.1 (a) During what year does the point of "diminishing returns" (i.e., the inflection point) appear to take place? During the year ________________ (b) If the best fitting logistic function for this data is P=(69)/(1+340e−0.67t) (where t is years since 1978) what is the limiting value (as t gets very large)? _____________________ 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 1985?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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 ficticious).
| Year | 1978 | 1979 | 1980 | 1981 | 1982 | 1983 | 1984 | 1985 | 1986 | 1987 | 1988 | 1989 | 1990 | 1991 |
| % having VCR | 0.2 | 0.4 | 0.8 | 1.5 | 3.0 | 5.1 | 9.8 | 17.2 | 27.9 | 38.3 | 48.2 | 56.8 | 59.7 | 62.1 |
(a) During what year does the point of "diminishing returns" (i.e., the inflection point) appear to take place?
During the year ________________
(b) If the best fitting logistic function for this data is
P=(69)/(1+340e−0.67t)
(where t is years since 1978) what is the limiting value (as t gets very large)?
_____________________ 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 1985?
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