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 2.5 5.2 9.4 16.5 24.5 35.6 44.4 53.7 55.0 63.0 (a) During what year does the point of "diminishing returns" (i.e., the inflection point) appear to take place? (b) If the best fitting logistic function for this data is

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 2.5 5.2 9.4 16.5 24.5 35.6 44.4 53.7 55.0 63.0 (a) During what year does the point of "diminishing returns" (i.e., the inflection point) appear to take place? (b) If the best fitting logistic function for this data is

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 4BGP

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Question

The following table gives the percentage, PP, 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	2.5	5.2	9.4	16.5	24.5	35.6	44.4	53.7	55.0	63.0

(a) During what year does the point of "diminishing returns" (i.e., the inflection point) appear to take place?

(b) If the best fitting logistic function for this data is

P=63/1+350e^−0.68t

(where tt is years since 1978) what is the limiting value (as tt gets very large)?

(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 1983?

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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