Use the table below to answer questions 4–6.
The table shows the annual consumption of cheese per person in the United States for selected years in the 20th century. Note that the year 1900 corresponds to x = 0.
Year
Pounds
Consumed
1908
5.027
1923
8.768
1960
12.29
1981
15.485
What cubic model best fits this data?(1 point)
Responses
y = –0.0000541x3 + 0.00789x2 – 0.452x – 1.888
y = –0.0000541 x 3 + 0.00789 x 2 – 0.452 x – 1.888
y = –0.0000541x3 – 0.00789x2 – 0.452x + 1.888
y = –0.0000541 x 3 – 0.00789 x 2 – 0.452 x + 1.888
y = 0.00789x3 – 0.0000541x2 + 1.888x + 0.452
y = 0.00789 x 3 – 0.0000541 x 2 + 1.888 x + 0.452
y = 0.0000541x3 – 0.00789x2 + 0.452x + 1.888
y = 0.0000541x3 – 0.00789x2 + 0.452x + 1.888
To determine the cubic model that best fits the data, we need to consider the coefficients of the x terms. Looking at the given options, the cubic model that fits the data is:
y = –0.0000541x^3 + 0.00789x^2 – 0.452x – 1.888
To determine the cubic model that best fits the given data, we need to compare the coefficients and constants of the four given options with the data points in the table.
To fit the cubic model, we need to consider the general form: y = ax^3 + bx^2 + cx + d, where a, b, c, and d are coefficients that we need to determine.
Let's analyze the given data points and try to match them with the options:
Given data points:
- (1908, 5.027)
- (1923, 8.768)
- (1960, 12.29)
- (1981, 15.485)
Option 1: y = –0.0000541x^3 + 0.00789x^2 – 0.452x – 1.888
Comparing the coefficients, this option does not match the given data points accurately.
Option 2: y = –0.0000541x^3 + 0.00789x^2 – 0.452x – 1.888
This option has the same equation as option 1. Therefore, it also does not accurately match the given data points.
Option 3: y = –0.0000541x^3 – 0.00789x^2 – 0.452x + 1.888
Comparing the coefficients, this option does not match the given data points accurately.
Option 4: y = 0.0000541x^3 – 0.00789x^2 + 0.452x + 1.888
Comparing the coefficients, this option matches the given data points accurately.
Based on the analysis, the cubic model that best fits the given data is:
y = 0.0000541x^3 – 0.00789x^2 + 0.452x + 1.888