Choose differential equation that you believe best models the rate of change of the amount of salt in the mixing tank problem below. A tank initial contains 100 gallons of brine that has 200 pounds of salt. Brine containing 1/2 pound of salt per gallon enters the tank at a rate of 20 gallons per minute, and the perfectly mixed solution leaves the tank at a rate of 30 gallons per minute. dS A. dt 30S 10 - %3D 100–10t dS 30S 10 %3D dt 100 dS 10S C. dt 20 100–10t dS 30S dt 100–10t || B. D.
Choose differential equation that you believe best models the rate of change of the amount of salt in the mixing tank problem below. A tank initial contains 100 gallons of brine that has 200 pounds of salt. Brine containing 1/2 pound of salt per gallon enters the tank at a rate of 20 gallons per minute, and the perfectly mixed solution leaves the tank at a rate of 30 gallons per minute. dS A. dt 30S 10 - %3D 100–10t dS 30S 10 %3D dt 100 dS 10S C. dt 20 100–10t dS 30S dt 100–10t || B. D.
Calculus: Early Transcendentals
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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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Transcribed Image Text:Choose differential equation that you believe best models the rate of change of the amount of salt in
the mixing tank problem below.
A tank initial contains 100 gallons of brine that has 200 pounds of salt. Brine containing 1/2 pound of
salt per gallon enters the tank at a rate of 20 gallons per minute, and the perfectly mixed solution
leaves the tank at a rate of 30 gallons per minute.
dS
A.
dt
30S
10 -
%3D
100–10t
dS
30S
10
%3D
dt
100
dS
10S
C.
dt
20
100–10t
dS
30S
dt
100–10t
||
B.
D.
Expert Solution
Step 1
We need to determine which of the given equations best models the rate of change of the amount of salt in the mixing tank.
So first we need to determine the differential equation modelling the given requirement.
Let S be the amount pf salts in the pound at time t. Then we can represent the above situation by following diagram.
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