As the average service rate μ increases, the shape of the negative exponential distribution of service times

A) grows steadily steeper without limit.
B) has an ever steeper slope that eventually turns positive.
C) becomes less gently curved as it moves ever closer to the graph origin.
D) takes on a more uniform slope over a wide range of service times.
E) changes in appearance from convex to concave.

As the service rate increases, the average service time decreases, and so the negative exponential distribution becomes less gently curved and moves closer to the y-axis (graph origin). This is because there is less variability in service times as the service rate increases, leading to a narrower distribution. However, the shape remains negatively skewed and does not become uniform or switch to a positive slope.