A tank contains 80 gallons (gal) of pure water. A brine solution with 2 Ib/gal of salt enters at 2 gal/min, and the well-stirred mixture leaves at the same rate. Find (a) the amount of salt in the tank at any time, and (b) the time at which the brine leaving will contain 1 Ib/gal of salt.

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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1. A tank contains 80 gallons (gal) of pure water. A brine solution with 2 lb/gal
of salt enters at 2 gal/min, and the well-stirred mixture leaves at the same
rate. Find (a) the amount of salt in the tank at any time, and (b) the time
at which the brine leaving will contain 1 Ib/gal of salt.
2. In connection to problem 1, (a) determine the limiting value for the amount
of salt in the tank after a long time. (b) How much time must pass before
the amount of salt in the tank reaches 80 % of this limiting value?
Transcribed Image Text:1. A tank contains 80 gallons (gal) of pure water. A brine solution with 2 lb/gal of salt enters at 2 gal/min, and the well-stirred mixture leaves at the same rate. Find (a) the amount of salt in the tank at any time, and (b) the time at which the brine leaving will contain 1 Ib/gal of salt. 2. In connection to problem 1, (a) determine the limiting value for the amount of salt in the tank after a long time. (b) How much time must pass before the amount of salt in the tank reaches 80 % of this limiting value?
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