Per capita coffee consumption in the U.S. fluctuates over time but is greater here than anywhere else in the world. The number of cups f(x) consumed per adult per day in a given year x, with the year 1955 corresponding to x=0, is given by the mathematical model f(x)=2.77+0.0848.x-0.00832x² + 0.000144x³ . a. Use methods of calculus to determine the year in which coffee consumption was least during the period from 1955 to 1994. b. Use methods of calculus to determine the year in which coffee consumption was the greatest during the same period. What was the daily coffee consumption per adult in the U.S. at that time? c. Use the methods of calculus to determine the year in which coffee consumption was decreasing at the greatest rate (during the same time period). d. Graph y= f(x) for the years 1955 to 1994. Does your graph support your answers above? If not, explain any differences.
Per capita coffee consumption in the U.S. fluctuates over time but is greater here than anywhere else in the world. The number of cups f(x) consumed per adult per day in a given year x, with the year 1955 corresponding to x=0, is given by the mathematical model f(x)=2.77+0.0848.x-0.00832x² + 0.000144x³ . a. Use methods of calculus to determine the year in which coffee consumption was least during the period from 1955 to 1994. b. Use methods of calculus to determine the year in which coffee consumption was the greatest during the same period. What was the daily coffee consumption per adult in the U.S. at that time? c. Use the methods of calculus to determine the year in which coffee consumption was decreasing at the greatest rate (during the same time period). d. Graph y= f(x) for the years 1955 to 1994. Does your graph support your answers above? If not, explain any differences.
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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I only need part D answered.
The answers for a-c are:
A = 569.140502
B = 367.212757
C = 31.4764215
Transcribed Image Text:Per capita coffee consumption in the U.S. fluctuates over time but is greater here than
anywhere else in the world. The number of cups f(x) consumed per adult per day in a given
year x, with the year 1955 corresponding to x=0, is given by the mathematical model
f(x) = 2.77+0.0848.x-0.00832x² + 0.000144.x³ .
a. Use methods of calculus to determine the year in which coffee consumption was least
during the period from 1955 to 1994.
b. Use methods of calculus to determine the year in which coffee consumption was the
greatest during the same period. What was the daily coffee consumption per adult in
the U.S. at that time?
c. Use the methods of calculus to determine the year in which coffee consumption was
decreasing at the greatest rate (during the same time period).
d. Graph y= f(x) for the years 1955 to 1994. Does your graph support your answers
above? If not, explain any differences.
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