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.
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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Transcribed Image Text: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.
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