Chapter 1, Problem 42P

A thermostat control with dial marking from 0 to 100 is used to regulate the temperature of an oil bath. To calibrate the thermostat, the data for the temperature $T\left(°\text{F}\right)$ versus the dial setting R was obtained as shown in the table below:

The relationship between the temperature Tin Fahrenheit and the dial setting R satisfies the linear equation $T\left(°\text{F}\right)=aR+b$. (a) Using the given data, find the equation of the line relating the temperature to the dial setting.

(h) Sketch the graph of $T\left(°\text{F}\right)$ as a function of R, and clearly indicate a and h on your graph.

(c) Calculate the thermostat setting needed to obtain a temperature of

320°F.