Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). A B Suppose: The vat contains 160 gallons of liquid, which never changes. Sugar water with a concentration of 4 tablespoons/gallon flows through pipe A into the vat at the rate of 20 gallons/minute. Sugar water with a concentration of 1 tablespoons/gallon flows through pipe B into the vat at the rate of 35 gallons/minute. The liquid in the vat is kept well-mixed. Sugar water leaves the vat through pipe C at the rate of 55 gallons/minute. Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes. (A) Write the DE model for the time rate of change of sugar in the vat: ds dt (B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your function will have an arbitrary constant K in it. Assume that K > 0. S(t)= (C) Suppose that there are 28 tablespoons of sugar in the vat at t=0. How many tablespoons will be present 4 minutes later? tablespoons
Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). A B Suppose: The vat contains 160 gallons of liquid, which never changes. Sugar water with a concentration of 4 tablespoons/gallon flows through pipe A into the vat at the rate of 20 gallons/minute. Sugar water with a concentration of 1 tablespoons/gallon flows through pipe B into the vat at the rate of 35 gallons/minute. The liquid in the vat is kept well-mixed. Sugar water leaves the vat through pipe C at the rate of 55 gallons/minute. Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes. (A) Write the DE model for the time rate of change of sugar in the vat: ds dt (B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your function will have an arbitrary constant K in it. Assume that K > 0. S(t)= (C) Suppose that there are 28 tablespoons of sugar in the vat at t=0. How many tablespoons will be present 4 minutes later? tablespoons
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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Transcribed Image Text:Consider a large vat containing sugar water that is to be made into soft drinks (see figure below).
A
B
Suppose:
The vat contains 160 gallons of liquid, which never changes.
• Sugar water with a concentration of 4 tablespoons/gallon flows through pipe A into the vat at the
rate of 20 gallons/minute.
Sugar water with a concentration of 1 tablespoons/gallon flows through pipe B into the vat at the
rate of 35 gallons/minute.
• The liquid in the vat is kept well-mixed.
• Sugar water leaves the vat through pipe C at the rate of 55 gallons/minute.
Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes.
(A) Write the DE model for the time rate of change of sugar in the vat:
ds
dt
(B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your
function will have an arbitrary constant K in it. Assume that K > 0.
S(t)=
(C) Suppose that there are 28 tablespoons of sugar in the vat at t = 0. How many tablespoons will be
present 4 minutes later?
tablespoons
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