Initially 9 grams of salt are dissolved into 7 liters of water. Brine wi grams per liter is added at a rate of 5 liters per minute. The tank is liters per minute. a) Let x be the amount of salt, in grams, in the solution after t min formula for the rate of change in the amount of salt, dx/dt, in terr solution x. dx dt b) Find a formula for the amount of salt, in grams, after t minutes
Initially 9 grams of salt are dissolved into 7 liters of water. Brine wi grams per liter is added at a rate of 5 liters per minute. The tank is liters per minute. a) Let x be the amount of salt, in grams, in the solution after t min formula for the rate of change in the amount of salt, dx/dt, in terr solution x. dx dt b) Find a formula for the amount of salt, in grams, after t minutes
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:Initially 9 grams of salt are dissolved into 7 liters of water. Brine with concentration of salt 8
grams per liter is added at a rate of 5 liters per minute. The tank is well mixed and drained at 5
liters per minute.
a) Let x be the amount of salt, in grams, in the solution after t minutes have elapsed. Find a
formula for the rate of change in the amount of salt, dx/dt, in terms of the amount of salt in the
solution x.
dx
dt
b) Find a formula for the amount of salt, in grams, after t minutes have elapsed.
x(t) =
c) How long must the process continue until there are exactly 40 grams of salt in the tank?
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