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The amount of water in a storage tank, in gallons, is modeled by a continuous and differentiable function on the time interval 0

The amount of water in a storage tank, in gallons, is modeled by a continuous and differentiable function on the time interval 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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The amount of water in a storage tank, in gallons, is modeled by a continuous and differentiable function on the time interval 0 <t< 10, where t is measured in hours. In this model, the rates are given as follows: 3. The rate at which water enters the tank is f(t) = 100t? sin(vt) gallons per hour for 0 <t < 10. The rate at which water leaves the tank is g(t) = 1000x gallons per hour. а) Find f (2) and indicate correct units. Is the amount of water in the tank increasing or decreasing at t = The rate at which the amount of water in the tank is changing is a(t) = f(t) – g(t). Find a'(5) and b) 2? Justify your answer. c) indicate correct units.
Transcribed Image Text:The amount of water in a storage tank, in gallons, is modeled by a continuous and differentiable function on the time interval 0 <t< 10, where t is measured in hours. In this model, the rates are given as follows: 3. The rate at which water enters the tank is f(t) = 100t? sin(vt) gallons per hour for 0 <t < 10. The rate at which water leaves the tank is g(t) = 1000x gallons per hour. а) Find f (2) and indicate correct units. Is the amount of water in the tank increasing or decreasing at t = The rate at which the amount of water in the tank is changing is a(t) = f(t) – g(t). Find a'(5) and b) 2? Justify your answer. c) indicate correct units.
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