Answer all parts At the hummingbird food factory, hot water containing 1/3 of a pound of sugar per gallon of liquid is poured intoa giant mixing tank at a rate of 6 gallons per minute. The tank, which initially contains a priming solution of 5pounds of sugar dissolved in 1l gallons of water, is kept well-mixed and that well-mixed solution leaves the tankat a rate of 7 gallons per minute. Set up, but do not solve, an initial value problem (i.e., a rate of change equationwith an initial condition) that models the amount of sugar in the tank as a function of time.Reach 1: Point out exactly where the assumption that the liquid in the tank is kept well-mixed is reflected in yourequation above. Explain briefly.Reach 2: After 10 minutes, a change occurs in the situation described above: a leak develops in the tank, resultingin an additional 1 gallon of well-mixed solution leaving the tank each minute. At the same time, a source of purewater is added to the tank, at a rate of 2 gallons per minute. All else remains the same. Use a different variableto represent the amount of sugar in this "new" leaky tank, and let t = 0 correspond to the time the leak started.Write down an initial value problem corresponding to the amount of sugar in the new leaky tank. (Note: you donot need to solve the original problem in order to do this part.)

At the hummingbird food factory, hot water containing 1/3 of a pound of sugar per gallon of liquid is poured into a giant mixing tank at a rate of 6 gallons per minute. The tank, which initially contains a priming solution of 5 pounds of sugar dissolved in 11 gallons of water, is kept well-mixed and that well-mixed solution leaves the tank at a rate of 7 gallons per minute. Set up, but do not solve, an initial value problem (i.e., a rate of change equation with an initial condition) that models the amount of sugar in the tank as a function of time.

At the hummingbird food factory, hot water containing 1/3 of a pound of sugar per gallon of liquid is poured into a giant mixing tank at a rate of 6 gallons per minute. The tank, which initially contains a priming solution of 5 pounds of sugar dissolved in 11 gallons of water, is kept well-mixed and that well-mixed solution leaves the tank at a rate of 7 gallons per minute. Set up, but do not solve, an initial value problem (i.e., a rate of change equation with an initial condition) that models the amount of sugar in the tank as a function of time.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.7: Exponential And Logarithmic Models

Problem 23SE: A substance has a half-life of 2.045 minutes. If the initial amount of the substance was 132.8...

See similar textbooks