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to approximate the (c) It is known that G'(5) = 0.5. Use the locally linear approximation for G at time t = amount of gasoline in the storage tank at time t = 7. Is this approximation an overestimate or an underestimate for the actual amount of gasoline in the storage tank at time t = 7? Give a reason for your answer. 100t (d) The rate at which gasoline flows out of the storage tank into trucks at time t can be modeled by the function R defined by R(t) = +² +4² where t is measured in hours, and R(t) is measured in thousands of gallons. Based on the model, at what time t, for 0 ≤ t ≤ 10, is the rate at which gasoline flows out of the storage tank an absolute maximum? Justify your answer.

to approximate the (c) It is known that G'(5) = 0.5. Use the locally linear approximation for G at time t = amount of gasoline in the storage tank at time t = 7. Is this approximation an overestimate or an underestimate for the actual amount of gasoline in the storage tank at time t = 7? Give a reason for your answer. 100t (d) The rate at which gasoline flows out of the storage tank into trucks at time t can be modeled by the function R defined by R(t) = +² +4² where t is measured in hours, and R(t) is measured in thousands of gallons. Based on the model, at what time t, for 0 ≤ t ≤ 10, is the rate at which gasoline flows out of the storage tank an absolute maximum? Justify your answer.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(c) It is known that G'(5) = 0.5. Use the locally linear approximation for G at time t = 5 to approximate the amount of gasoline in the storage tank at time t = 7. Is this approximation an overestimate or an underestimate for the actual amount of gasoline in the storage tank at time t = 7? Give a reason for your answer. (d) The rate at which gasoline flows out of the storage tank into trucks at time t can be modeled by the function R defined by R(t) = where t is measured in hours, and R(t) is measured in thousands of gallons. Based on the model, at what time t, for 0 < t < 10, is the rate at which gasoline flows out of the storage tank an absolute maximum? Justify your answer. 100t t² +4,
Transcribed Image Text:(c) It is known that G'(5) = 0.5. Use the locally linear approximation for G at time t = 5 to approximate the amount of gasoline in the storage tank at time t = 7. Is this approximation an overestimate or an underestimate for the actual amount of gasoline in the storage tank at time t = 7? Give a reason for your answer. (d) The rate at which gasoline flows out of the storage tank into trucks at time t can be modeled by the function R defined by R(t) = where t is measured in hours, and R(t) is measured in thousands of gallons. Based on the model, at what time t, for 0 < t < 10, is the rate at which gasoline flows out of the storage tank an absolute maximum? Justify your answer. 100t t² +4,
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
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
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