Question

The table shows the annual consumption of cheese per person in the United States for selected years in the 20th century. Let x = number of years since 1900, and y = pounds per person. What cubic model best fits this data? YearPounds Consumed. 19021.959. 19246.373. 19467.29. 198215.817. A. y = 0.00989x3 - 0.0000872x2 + 1.192x + 0.403. B. y = -0.0000872x3 + 0.00989x2 - 0.403x - 1.192. C. y = -0.0000872x3 - 0.00989x2 - 0.403x + 1.192. D. y = 0.0000872x3 - 0.00989x2 + 0.403x + 1.192

Answer 1

To see what model best represents this data we have to plug in the values for x and y:
Model D :
x = 2, y = 1.959
y = 0.0000872 · 2³ - 0.00989 · 2² + 0.403 · 2 + 1.192 = 1.968
....   ...
x = 82,  y = 15.817
y = 0.000873 · 82³ - 0.00989 · 82² + 0.403 · 82 + 1.192 = 15.818
Answer:
D ) y = 0.0000872 x² - 0.00989 x² + 0.403 x + 1.192