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11 In the diagram, a tank initially contains 1000 litres of pure water. Salty water begins pouring into the tank from a pipe, and a stirring blade ensures that it is always completely mixed with the pure water. A second pipe draws the mixture off at the same rate, so that there is always a total of 1000 litres in the tank. a If the salty water entering the tank contains 2 grams of salt per litre, and is flowing in at the constant rate of w litres/min, how much salt is entering the tank per minute? Salt water Water and 1000 L tank salt water mixture b If there are Q grams of salt in the tank at time t, how much salt is in 1 litre at time t? c Hence write down the amount of salt leaving the tank per minute. d Use the previous parts to show that dQ dt W = (Q - 2000). 1000 wt e Show that Q: f = 2000 + Ae 1000 is a solution of this differential equation. Determine the value of A. g What happens to Q as t→ 00? h If there is 1 kg of salt in the tank after 5 hours, find w.

11 In the diagram, a tank initially contains 1000 litres of pure water. Salty water begins pouring into the tank from a pipe, and a stirring blade ensures that it is always completely mixed with the pure water. A second pipe draws the mixture off at the same rate, so that there is always a total of 1000 litres in the tank. a If the salty water entering the tank contains 2 grams of salt per litre, and is flowing in at the constant rate of w litres/min, how much salt is entering the tank per minute? Salt water Water and 1000 L tank salt water mixture b If there are Q grams of salt in the tank at time t, how much salt is in 1 litre at time t? c Hence write down the amount of salt leaving the tank per minute. d Use the previous parts to show that dQ dt W = (Q - 2000). 1000 wt e Show that Q: f = 2000 + Ae 1000 is a solution of this differential equation. Determine the value of A. g What happens to Q as t→ 00? h If there is 1 kg of salt in the tank after 5 hours, find w.

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 In the diagram, a tank initially contains 1000 litres of pure water. Salty water begins pouring into the tank from a pipe, and a stirring blade ensures that it is always completely mixed with the pure water. A second pipe draws the mixture off at the same rate, so that there is always a total of 1000 litres in the tank. a If the salty water entering the tank contains 2 grams of salt per litre, and is flowing in at the constant rate of w litres/min, how much salt is entering the tank per minute? Salt water Water and 1000 L tank salt water mixture b If there are Q grams of salt in the tank at time t, how much salt is in 1 litre at time t? c Hence write down the amount of salt leaving the tank per minute. d Use the previous parts to show that dQ dt W = (Q - 2000). 1000 wt e Show that Q: f = 2000 + Ae 1000 is a solution of this differential equation. Determine the value of A. g What happens to Q as t→ 00? h If there is 1 kg of salt in the tank after 5 hours, find w.
Transcribed Image Text:11 In the diagram, a tank initially contains 1000 litres of pure water. Salty water begins pouring into the tank from a pipe, and a stirring blade ensures that it is always completely mixed with the pure water. A second pipe draws the mixture off at the same rate, so that there is always a total of 1000 litres in the tank. a If the salty water entering the tank contains 2 grams of salt per litre, and is flowing in at the constant rate of w litres/min, how much salt is entering the tank per minute? Salt water Water and 1000 L tank salt water mixture b If there are Q grams of salt in the tank at time t, how much salt is in 1 litre at time t? c Hence write down the amount of salt leaving the tank per minute. d Use the previous parts to show that dQ dt W = (Q - 2000). 1000 wt e Show that Q: f = 2000 + Ae 1000 is a solution of this differential equation. Determine the value of A. g What happens to Q as t→ 00? h If there is 1 kg of salt in the tank after 5 hours, find w.
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