- #1

the7joker7

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## Homework Statement

A tank contains 90 kg of salt and 2000 L of water. Pure water enters a tank at the rate 12 L/min. The solution is mixed and drains from the tank at the rate 6 L/min.

Find the amount of salt in the tank after 1.5 hours.

## Homework Equations

Assorted Calculus stuff.

## The Attempt at a Solution

rate in = (.045kg per L)(12L per min) = .54kg/min

rate out = (y(t)/2000 kg per L)(6L per min) = (y(t))/(333.33)

dy/dt = .54 - ((y(t))/333.33) = (180 - y(t))/333.33

int(dy/(180 - y)) = int(dt/333.33)

-ln(180 - y) = t/333.33 + C

y(0) = 90

So -ln(90) = C

-ln(180 - y) = t/333.33 - ln(90)

180 - y = 90e^(-t/333.33)

y(t) = 180 - 90e^(t/333.33)

y(90) = 62.103

**Actual Answer:**

70.8661417323