When the price of an essential commodity rises rapidly, consumption drops slowly at first. If the price continues to rise, however, a “tipping” point may be reached, at which consumption takes a sudden substantial drop. Suppose the accompanying graph shows the consumption of gasoline, G(t), in millions of gallons, in a certain area. We assume that the price is rising rapidly. Here t is the time in months after the price began rising.
(a) Sketch a graph of the rate of change in consumption as a function of time.

(b) When does the “tipping” point occur? What is the instantaneous rate of change in consumption of gas at that point?

Transcribed Image Text:

G(t) 4 3.5 3 2.5 2 1.5 1 0.5 0 4 (12,3) f (16, 1.5) 8 12 + 16 (16, 2) H 20 24