(a) Let s(t) be the amount of salt in the tank at time t. Find a differential equation governing s(t).
(a) Let s(t) be the amount of salt in the tank at time t. Find a differential equation governing s(t).
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Transcribed Image Text:A miracle tank of infinite volume is initially empty. Salt solution is pumped into
the tank at a rate of 3L/min and drains out of the tank at a rate of 1L/min. The
concentration of the solution being pumped in depends on time linearly: the con-
centration at time t is tkg/L.
(a)
Let s(t) be the amount of salt in the tank at time t. Find a differential
equation governing s(t).
(b)
The tank was discovered to contain an unknown amount of (dried)
salt at time zero. However, at 1 minute, the tank was determined to contain 2
kg of salt. Find s(t) explicitly.
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