Problem 2 On most state highways, the fine for speeding depends on the speed of the car. On a certain state highway, the fine for driving 70 mph is $25 and the fine for driving 85 mph is $100. On this particular road, when a car brakes suddenly, the function
S(d)=40d‾‾‾‾√ (square root 40d) can be used to approximate the speed of a car (in mph) when it leaves a skid mark of length d feet on the road.

Part a)
Using the information provided, write a linear equation that represents the fine for speeding, F, as a function of the speed in mph on the state highway. (Remember: Identify your input and output variables, use proper notation, and show your work.)

Part b)
Find (F∘S)(d) and explain what this function does in context of the problem.