Chapter 3.2, Problem 12E

Reminder Round all answer to two decimal places unless otherwise indicated.

Speed of Sounds The speed of sound in air changes with the temperature. When the temperature $T$ is $32$ degrees Fahrenheit, the speed $S$ of sound is $1087.5$ feet per second. For each degree increase in temperature, the speed of sound increases by $1.1$ feet per second.

a. Explain why speed $S$ is a linear function of temperature $T.$ Identify the slope of the function.

b. Use a formula to express $S$ as a linear function of $T.$

c. Solve for $T$ in the equation from part $\text{b}$ to obtain a formula for temperature $T$ as a linear function of speed $S.$

d. Explain in practical terms the meaning of the slope of the function you found in part $\text{c}\text{.}$