7. An outdoor swimming pool loses 0.05% of its water volume every day it is in use, due to losses from evaporation and from excited swimmers who splash water. A system is available to continually replace water at a rate of G gallons per day of use. (a) Find an expression, in terms of G, for the equilibrium volume of the pool. Sketch a few graphs for the volume V(t), including all possible types of solutions. (b) If the pool volume is initially 1% above its equilibrium value, find an expression for V(t). (c) What is the replacement rate G required to maintain 12 000 gal of water in the pool?
7. An outdoor swimming pool loses 0.05% of its water volume every day it is in use, due to losses from evaporation and from excited swimmers who splash water. A system is available to continually replace water at a rate of G gallons per day of use. (a) Find an expression, in terms of G, for the equilibrium volume of the pool. Sketch a few graphs for the volume V(t), including all possible types of solutions. (b) If the pool volume is initially 1% above its equilibrium value, find an expression for V(t). (c) What is the replacement rate G required to maintain 12 000 gal of water in the pool?
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:7. An outdoor swimming pool loses 0.05% of its water volume every day it is in use, due to losses
from evaporation and from excited swimmers who splash water. A system is available to
continually replace water at a rate of G gallons per day of use.
(a) Find an expression, in terms of G, for the equilibrium volume of the pool. Sketch a few graphs
for the volume V (t), including all possible types of solutions.
(b) If the pool volume is initially 1% above its equilibrium value, find an expression for V(t).
(c) What is the replacement rate G required to maintain 12,000 gal of water in the pool?
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