Use the data from Exercise and use quadratic regression to find a function g that models these data.
(a) Give the function.
(b) Graph the function with the data points.
(c) Find the estimated tuition with this model for the year 2015.
Exercise
The following table shows the average cost of tuition and fees at private colleges in various years.’
Table
Year | Cost |
1975 | 3672 |
1980 | 5470 |
1985 | 8885 |
1990 | 12,910 |
1995 | 17,208 |
2000 | 21,373 |
2005 | 26,908 |
2010 | 32,026 |
(a) Let x = 5 correspond to the year 1975. Find a quadratic function f(x) = a(x − h)2 + k that models these data using (5, 3672) as the vertex and the data for 2005.
(b) Estimate the average tuition and fees at private colleges in 2015.
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