Chapter 2.3, Problem 61E

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)

A mathematical model for the data is given by

$f\left(x\right)=-0.518x^2+33.3x-481$

(A) Complete the following table. Round values of $f\left(x\right)$ to one decimal place

(B) Sketch the graph of $f$ and the mileage data in the same coordinate system.

(C) Use the modeling function $f\left(x\right)$ to estimate the mileage for a tire pressure of $31\text{lbs/sq}\text{in}\text{.}$ and for $\text{35}\text{lbs/sq}\text{in}\text{.}$ Round answers to two decimal places.

(D) Write a brief description of the relationship between tire pressure and mileage.