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A 75-gallon tank initially contains 75 gallons of brine with a concentration of 2 pounds of salt per gallon. Pure water enters the tank at a rate of 2 gallons per minute. The tank is kept thoroughly mixed and drains at a rate of 7 gallons per minute. a) Write and solve an initial value problem to find a formula for the amount of salt in the tank after t minutes. b) For what values of t is your formula valid? Explain why it is not valid outside that range. c) Use your formula to predict the amount of salt in the tank after 5 minutes. Round your answer as you see fit.

A 75-gallon tank initially contains 75 gallons of brine with a concentration of 2 pounds of salt per gallon. Pure water enters the tank at a rate of 2 gallons per minute. The tank is kept thoroughly mixed and drains at a rate of 7 gallons per minute. a) Write and solve an initial value problem to find a formula for the amount of salt in the tank after t minutes. b) For what values of t is your formula valid? Explain why it is not valid outside that range. c) Use your formula to predict the amount of salt in the tank after 5 minutes. Round your answer as you see fit.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Problem Description A 75-gallon tank initially contains 75 gallons of brine with a concentration of 2 pounds of salt per gallon. Pure water enters the tank at a rate of 2 gallons per minute. The tank is kept thoroughly mixed and drains at a rate of 7 gallons per minute. ### Tasks a) **Write and solve an initial value problem to find a formula for the amount of salt in the tank after \( t \) minutes.** b) **For what values of \( t \) is your formula valid? Explain why it is not valid outside that range.** c) **Use your formula to predict the amount of salt in the tank after 5 minutes. Round your answer as you see fit.**
Transcribed Image Text:### Problem Description A 75-gallon tank initially contains 75 gallons of brine with a concentration of 2 pounds of salt per gallon. Pure water enters the tank at a rate of 2 gallons per minute. The tank is kept thoroughly mixed and drains at a rate of 7 gallons per minute. ### Tasks a) **Write and solve an initial value problem to find a formula for the amount of salt in the tank after \( t \) minutes.** b) **For what values of \( t \) is your formula valid? Explain why it is not valid outside that range.** c) **Use your formula to predict the amount of salt in the tank after 5 minutes. Round your answer as you see fit.**
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