Chapter 2.6, Problem 30E

Technology Exercises

Consumption of Coffee in the U.S. Coffee consumption in the United States is greater on a per capita basis than anywhere else in the world. However, due to price fluctuations of coffee beans and worries over the health effects of caffeine, coffee consumption has varied considerably over the years. According to data published in The Wall Street Journal, the number of cups $f(x)$ consumed daily per adult in year $x$ (with $1955$ corresponding to $x=0$) is given by the mathematical model

$f(x)=2.77+0.0848x-0.00832x^2+0.000144x^3$

a. Graph $y=f(x)$ to show daily coffee consumption from $1955$ through $1994$.

b. Use $f\text{'}(x)$ to determine the year in which coffee consumption was least during this period. What was the daily coffee consumption at that time?

c. Use $f\text{'}(x)$ to determine the year in which coffee consumption was greatest during this period. What was the daily coffee consumption at that time?

d. Use $f\text{'}\text{'}(x)$ to determine the year in which coffee consumption was decreasing at the greatest rate.