When the price of an essential commodity (such as gasoline) rises rapidly, consu

Question

When the price of an essential commodity (such as gasoline) 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 time in months after the price began rising. Use the graph to find the following. a) lim_t rightarrow 12 G(t) = _____ b) lim_t rightarrow 16 G(t) = _____ c) G(16) = _____ d) The tipping point (in months) = _____

Explanation / Answer

a)

Lim t—> 12+ G(t) = 3

Lim t—> 12- G(t) = 3

since left hand limit and right hand limit are equal,

Lim t—> 12 G(t) = 3

Answer: 3

b)

Lim t—> 16+ G(t) = 1.5

Lim t—> 16- G(t) = 2

since left hand limit and right hand limit are not equal,

Lim t—> 12 does not exist

Answer: does not exist

c)

G(16) = 1.5

d)

tipping point is price is 16

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