Transcribed Image Text:t (hours)
0
1
5 8 10
G(t) (thousands of gallons) 22 18.5 19.5 22 24
A gasoline storage tank is filled by a pipeline from a refinery. At the same time, gasoline flows from the tank into
trucks that will make deliveries to gasoline stations. The amount of gasoline in the storage tank at time t is given
by the twice-differentiable function G, where t is measured in hours and 0 ? t ? 10. Values of G(t), in
thousands of gallons, at selected times t are given in the table above. It is known that G”(t) > 0 for 5 ? t < 10
(a) Use the data in the table to estimate the rate of change of the amount of gasoline in the storage tank at time
t=3 hours. Show the computations that lead to your answer. Indicate units of measure.
(b) For 0 < t < 10, is there a time t at which G(t) is increasing at a rate of 0.2 thousand gallons per hour?
Justify your answer.
0
1
5 8 10
G(t) (thousands of gallons) 22 18.5 19.5 22 24
A gasoline storage tank is filled by a pipeline from a refinery. At the same time, gasoline flows from the tank into
trucks that will make deliveries to gasoline stations. The amount of gasoline in the storage tank at time t is given
by the twice-differentiable function G, where t is measured in hours and 0 ? t ? 10. Values of G(t), in
thousands of gallons, at selected times t are given in the table above. It is known that G”(t) > 0 for 5 ? t < 10
(a) Use the data in the table to estimate the rate of change of the amount of gasoline in the storage tank at time
t=3 hours. Show the computations that lead to your answer. Indicate units of measure.
(b) For 0 < t < 10, is there a time t at which G(t) is increasing at a rate of 0.2 thousand gallons per hour?
Justify your answer.
