Can someone please explain and help me with this problem.
4. The table shows the annual consumption of cheese per person in the United States for selected years in the 20th century.
Year Pounds
Consumed
1908 5.027
1923 8.768
1960 12.29
1981 15.485
What cubic model best fits this data?
y = ¨C0.0000541x3 + 0.00789x2 ¨C 0.452x ¨C 1.888
y = ¨C0.0000541x3 ¨C 0.00789x2 ¨C 0.452x + 1.888
y = 0.00789x3 ¨C 0.0000541x2 + 1.888x + 0.452
y = 0.0000541x3 ¨C 0.00789x2 + 0.452x + 1.888
5. If you were going to use this model to estimate the amount of cheese consumed per person in 1976, would that prediction be considered interpolation or extrapolation?
interpolation
extrapolation
6. What is the domain of the graph for the data set?
1976
5.027 ¡Ü domain ¡Ü 15.485
1908 ¡Ü domain ¡Ü 1981
any year in the twentieth century
To determine the cubic model that best fits the given data, we need to analyze the given options and match them with the data points provided.
The given options are:
y = -0.0000541x^3 + 0.00789x^2 - 0.452x - 1.888
y = -0.0000541x^3 - 0.00789x^2 - 0.452x + 1.888
y = 0.00789x^3 - 0.0000541x^2 + 1.888x + 0.452
y = 0.0000541x^3 - 0.00789x^2 + 0.452x + 1.888
To determine which cubic model best fits the data, we need to compare the data points and see which model aligns with them.
The given data points are:
1908 - 5.027
1923 - 8.768
1960 - 12.29
1981 - 15.485
By analyzing the data points, we can observe that the data is increasing over time. This means that the coefficient of the x^3 term should be negative in order to capture this trend.
By analyzing the options, we can see that the cubic model y = -0.0000541x^3 + 0.00789x^2 - 0.452x - 1.888 best aligns with the given data points, as the coefficient of the x^3 term is negative.
Hence, the cubic model that best fits the data is y = -0.0000541x^3 + 0.00789x^2 - 0.452x - 1.888.
For question 5, if we were to use this model to estimate the amount of cheese consumed per person in 1976, that prediction would be considered extrapolation. This is because extrapolation involves making predictions outside of the range of the given data. In this case, the given data does not include 1976, so using the cubic model to estimate cheese consumption for that year would be extrapolating beyond the given data.
For question 6, the domain of the graph in the data set is determined by the range of years provided in the data. In this case, the domain of the graph would be 1908 ≤ domain ≤ 1981, as these are the years for which data is given.
To determine the cubic model that best fits the given data, we can analyze the given options and choose the one that closely matches the data points.
Looking at the options provided:
1. y = ¨C0.0000541x^3 + 0.00789x^2 ¨C 0.452x ¨C 1.888
2. y = ¨C0.0000541x^3 ¨C 0.00789x^2 ¨C 0.452x + 1.888
3. y = 0.00789x^3 ¨C 0.0000541x^2 + 1.888x + 0.452
4. y = 0.0000541x^3 ¨C 0.00789x^2 + 0.452x + 1.888
We should substitute the x-values (years) and check which equation gives us values closest to the corresponding y-values (pounds consumed).
By substituting the given years (1908, 1923, 1960, and 1981) into each equation, we can calculate the estimated pounds consumed and compare them to the given values.
After calculating the pounds consumed for each equation, we can compare them to the given values and see which equation produces the closest results. The equation with the closest values will be the cubic model that best fits the data.
For the second question:
Interpolation refers to estimating values within the given data range, while extrapolation refers to estimating values outside the given data range.
Since we are asked to estimate the amount of cheese consumed per person in 1976, which falls within the given years of the dataset (1908 - 1981), this prediction would be considered interpolation.
For the third question:
The domain of the graph for the given data set refers to the range of x-values (years) included in the dataset. In this case, the domain is specified as "any year in the twentieth century." Therefore, the domain of the graph is from 1900 to 1999.