The most expensive rates (in dollars per minute) for a 2-minute telephone call using a long-distance carrier are listed in the table. Long-Distance Telephone Rates Year 1982 1984 1985 1986 1987 1988 1989 1990 1995 2000 Rate, p (dollars per minute) 1.30 1.25 1.14 1.02 0.82 0.77 0.65 0.64 0.39 0.20 (a) Find the function for the quadratic model that gives the most expensive rates in dollars per minute for a 2-minute telephone call using a long-distance carrier, where x is the number of years 1980, with data from 2 ≤ x ≤ 20. (Round all numerical values to three decimal places.) p(x) = dollars per minute (b) Calculate the average of the most expensive rates from 1982 through 2000. (Round your answer to three decimal places.) $ per minute (c) Calculate the average rate of change of the most expensive rates from 1982 through 2000. (Round your answer to three decimal places.) per minute per year
The most expensive rates (in dollars per minute) for a 2-minute telephone call using a long-distance carrier are listed in the table. Long-Distance Telephone Rates Year 1982 1984 1985 1986 1987 1988 1989 1990 1995 2000 Rate, p (dollars per minute) 1.30 1.25 1.14 1.02 0.82 0.77 0.65 0.64 0.39 0.20 (a) Find the function for the quadratic model that gives the most expensive rates in dollars per minute for a 2-minute telephone call using a long-distance carrier, where x is the number of years 1980, with data from 2 ≤ x ≤ 20. (Round all numerical values to three decimal places.) p(x) = dollars per minute (b) Calculate the average of the most expensive rates from 1982 through 2000. (Round your answer to three decimal places.) $ per minute (c) Calculate the average rate of change of the most expensive rates from 1982 through 2000. (Round your answer to three decimal places.) per minute per year
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The most expensive rates (in dollars per minute) for a 2-minute telephone call using a long-distance carrier are listed in the table.
Long-Distance Telephone Rates
Year
1982
1984
1985
1986
1987
1988
1989
1990
1995
2000
Rate, p
(dollars per minute)
1.30
1.25
1.14
1.02
0.82
0.77
0.65
0.64
0.39
0.20
(a) Find the function for the quadratic model that gives the most expensive rates in dollars per minute for a 2-minute telephone call using a long-distance carrier, where x is the number of years
1980, with data from 2 ≤ x ≤ 20. (Round all numerical values to three decimal places.)
p(x) =
dollars per minute
(b) Calculate the average of the most expensive rates from 1982 through 2000. (Round your answer to three decimal places.)
$
per minute
(c) Calculate the average rate of change of the most expensive rates from 1982 through 2000. (Round your answer to three decimal places.)
per minute per year
Transcribed Image Text:The per capita consumption of commercially produced fresh vegetables in a certain country from 1980 through 2000 can be modeled as
v(t) = 0.092+² +0.710r + 149.551 pounds
where t is the number of years since 1980.
(a) What was the average per capita consumption of commercially produced fresh vegetables in the country between 1980 and 2000? (Round your answer to three decimal places.)
pounds
(b) What was the average rate of change in per capita consumption between 1980 and 2000? (Round your answer to two decimal places.)
pounds per year
(c) In which year was the per capita consumption closest to the average per capita consumption between 1980 and 2000? (Round your answer up to the nearest integer.)
(d) Illustrate the answers from parts (a), (b), and (c) on a graph of v.
v(t)
O
200
180
160
140
120
v(t)
200
180
160
140
120
Average rate
of change
Average value.
Average rate
of change
Average value
O
O
v(t)
200
180
160
140
120
v(t)
200
180
160
140
120
Average value
Average rate
of change
Average value
Average rate
of change
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