The attendance A (in millions) at NCAA womens college basketball games for the years 1994 through 2000 is shown in the table, where t represents the year, with t=4 corresponding to 1994.
year t attendance a
4 4.557
5 4.962
6 5.234
7 6.734
8 7.387
9 8.698
10 8.825
a. use the regresssion feature of a graphing utility to find the cubic model for the data.
b. use the graphing utility to create a scatter plot of the data. then graph of the model and the scatter plot in the same viewing window. how do they compare?
c. according to the model found in part (a) in what year did attendance reach 5.5 million?
d. according to the model found in part (a), in what year did attendance reach 8 million?
e. according to the right hand behavior of the model, will the attendance continue to increase? explain
a. To find the cubic model for the data using a graphing utility, follow these steps:
1. Input the data into the graphing utility, representing years (t) in the x-axis and attendance (a) in the y-axis.
2. Select the regression feature of the graphing utility.
3. Choose the cubic regression model option, as you want to find a cubic model for the data.
4. The graphing utility will calculate the coefficients of the cubic model equation, which represents the cubic relationship between years and attendance.
b. To create the scatter plot of the data and graph the model in the same viewing window, follow these steps:
1. Enter the data points into the graphing utility to create a scatter plot.
2. Plot the scatter plot of the data points.
3. Use the cubic model equation found in part (a) to generate the graph of the model.
4. Adjust the viewing window to display both the scatter plot and the model graph together.
To compare the scatter plot and the model graph, observe if the data points align with the curve of the model graph. If the data points fall close to or on the model curve, it indicates that the cubic model is a good fit for the data.
c. To determine the year when attendance reached 5.5 million according to the model found in part (a), substitute 5.5 million for the attendance (a) in the cubic model equation. Solve the equation to find the year (t) that corresponds to that attendance value.
d. Similarly, to find the year when attendance reached 8 million according to the model found in part (a), substitute 8 million for the attendance (a) in the cubic model equation and solve for the year (t).
e. To determine the right-hand behavior of the model and whether attendance will continue to increase, examine the coefficient of the highest power term in the cubic model equation. If the coefficient is positive, it indicates that as years increase, attendance will continue to increase.