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?
Year Pounds Consumed
1902 1.959
1924 6.373
1946 7.29
1982 15.817

A. y = 0.00989x^3 - 0.0000872x^2 + 1.192x + 0.403
B. y = -0.0000872x^3 + 0.00989x^2 - 0.403x - 1.192
C. y = -0.0000872x^3 - 0.00989x^2 - 0.403x + 1.192
D. y = 0.0000872x^3 - 0.00989x^2 + 0.403x + 1.192

Answer 1

y = 0.0000872x^3 - 0.00989x^2 + 0.403x + 1.192

Answer 2

Right answer:

D. y = 0.0000872x^3 - 0.00989x^2 + 0.403x + 1.192

In this problem, we have the annual consumption of cheese per person in the USA  for selected years in the 20th century. This is expressed in Pounds. The pound is a unit for measuring weight, used in several countries including the U.S and the U.K containing 16 ounces and equal to 0.454 kilograms. So, we also know that:

x = number of years since 1900

y = pounds per person

Option D is correct because we can replace each year by a number between 0 and 99, I mean:

1900 = 0

1901 = 1

1902 = 2

1903 = 3

1904 = 4, and so on.

Therefore:

1902 = 2

1924 = 24

1946 = 46

1982 = 82

By replacing these x-values in the equation we have that:

For x = 2:

y = 1902

For x = 24:

y = 6.373

For x = 46:

y = 7.29

For x = 82:

y = 15.817