4. During the production process at a local brewery, a batch of beer with 6% alcohol is pumped into a barrel containing a 500 gallon batch of beer with 4% alcohol at a rate of 5 gallons/minute. The resulting mixture is pumped out at the same rate. 6% Alcohol e 5 gal/min Mixture e 5 gal/min As the two batches mix, the total volume of pure alcohol in the barrel a(t) changes as a function of time and satisfies the following first-order differential equation and initial condition: da + 0.01a(t) = 0.3 dt a(0) = 20 gallons of alcohol a) Determine the transient solution, atrans(t)

4. During the production process at a local brewery, a batch of beer with 6% alcohol is pumped into a barrel containing a 500 gallon batch of beer with 4% alcohol at a rate of 5 gallons/minute. The resulting mixture is pumped out at the same rate. 6% Alcohol e 5 gal/min Mixture e 5 gal/min As the two batches mix, the total volume of pure alcohol in the barrel a(t) changes as a function of time and satisfies the following first-order differential equation and initial condition: da + 0.01a(t) = 0.3 dt a(0) = 20 gallons of alcohol a) Determine the transient solution, atrans(t)

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

b) Determine the steady-state solution, ass(t)
c) Determine the total solution a(t) subject to the given initial conditions.
d) Plot a(t) as a function of time for 0 <t < 240 min

4. During the production process at a local brewery, a batch of beer with 6% alcohol is pumped
into a barrel containing a 500 gallon batch of beer with 4% alcohol at a rate of 5 gallons/minute.
The resulting mixture is pumped out at the same rate.
| 6% Alcohol @5 gal/min
Mixture @ 5gal/min
As the two batches mix, the total volume of pure alcohol in the barrel a(t) changes as a
function of time and satisfies the following first-order differential equation and initial
condition:
da
+ 0.01a(t) = 0.3
dt
a(0) = 20 gallons of alcohol
%3D
a) Determine the transient solution, atrans(t)

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