The speed of a car prior to hard braking can be estimated by the length of the skid mark. One model claims that the speed S in mi/hr is S = √130ℓ, where ℓ is the length of the skid mark in feet and 50 ≤ ℓ ≤ 150.

In each exercise, a function and an interval of its independent variable are given. The endpoints of the interval are associated with the points P and Q on the graph of the function.

a. Sketch a graph of the function and the secant line through P and Q.

b. Find the slope of the secant line in part (a), and interpret your answer in terms of an average rate of change over the interval. Include units in your answer.