The number of automobile tire sales is dependent on several variables. In one study the relationship among annual tire sales S (in thousands of dollars), automobile registrations R (in millions), and personal disposable income I (in millions of dollars) was investigated. The results for three years are given in the table.

To describe the relationship among these variables, we can use the equation S = a + bR + cI, where the coefficients a, b, and c are constants that must be determined before the equation can be used.

(a) Substitute the values for S, R, and I for each year from the table into the equation S = a + bR + cI, and obtain three linear equations involving a, b, and c.

(b) Use a graphing calculator to solve this linear system for a, b, and c. Use matrix inverse methods.

(c) Write the equation for S using these values for the coefficients.

(d) If R = 117.6 and I = 310.73, predict S. (The actual value for S was 11,314.)

(e) If R = 143.8 and I = 829.06, predict S. (The actual value for S was 18,481.)

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10,170 112.9 307.5 15,305 132.9 621.63 21,289 155.2 1937.13