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?