Tire mileage. An automobile tire manufacturer collected the data in the table relating tire pressure x (in pounds per square inch) and mileage (in thousands of miles):
x | Mileage |
28 | 45 |
30 | 52 |
32 | 55 |
34 | 51 |
36 | 47 |
A mathematical model for the data is given by
f(x) = −0.518x2 + 33.3x − 481
(A) Complete the following table. Round values of f(x) to one decimal place.
x
Mileage
f(x)
28
45
30
52
32
55
34
51
36
47
(B) Sketch the graph of f and the mileage data in the same coordinate system.
(C) Use values of the modeling function rounded to two decimal places to estimate the mileage for a tire pressure of 31 lb/sq in. and for 35 lb/sq in.
(D) Write a brief description of the relationship between tire pressure and mileage.
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