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11. (Calculator) Fluid is pumped into a tank at a rate of 8 gal/min. At the same time, the fluid is leaking out of the tank at a rate of vt +1 gal/min, where 0

11. (Calculator) Fluid is pumped into a tank at a rate of 8 gal/min. At the same time, the fluid is leaking out of the tank at a rate of vt +1 gal/min, where 0

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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11. (Calculator) Fluid is pumped into a tank at a rate of 8 gal/min. At the same time, the fluid is leaking out of the tank at a rate of vt +1 gal/min, where 0<t<120 min. The tank initially contains 30 gallons of fluid. a) Find the number of gallons of fluid that leaked out of the tank fromt = 0 to t = 3 minutes. b) Find the number of gallons of fluid that are in the tank at exactly t= 3 minutes. (continued) c) Let A(t) represent the total number of gallons of fluid in the tank at any time t. Write a formula for A(t). d) Use calculus to determine when the tank has the most fluid in it on the interval 0<t<120. Justify your answer.
Transcribed Image Text:11. (Calculator) Fluid is pumped into a tank at a rate of 8 gal/min. At the same time, the fluid is leaking out of the tank at a rate of vt +1 gal/min, where 0<t<120 min. The tank initially contains 30 gallons of fluid. a) Find the number of gallons of fluid that leaked out of the tank fromt = 0 to t = 3 minutes. b) Find the number of gallons of fluid that are in the tank at exactly t= 3 minutes. (continued) c) Let A(t) represent the total number of gallons of fluid in the tank at any time t. Write a formula for A(t). d) Use calculus to determine when the tank has the most fluid in it on the interval 0<t<120. Justify your answer.
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