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## Homework Statement

A 400-gallon tank initially contains 200 gallons of water containing 2 parts per billion by weight of dioxin, an extremely potent carcinogen. Suppose water containing 5 parts per billion flows into the top of the tank at a rate of 4 gallons per minute. The water in the tank is kept well mixed, and 2 gallons per minute are removed from the bottom of the tank. How much dioxin is in the tank when the tank is full?

## Homework Equations

I'm going to use D(t) as the amount of dioxin.

## The Attempt at a Solution

dD/dt = (5)(4) - 2*(D(t)/(200+2t))

Using an integrating factor of t + 100, and the initial condition of D(0) = 2, I got that D(t) = (10t

^{2}+ 2000t + 200)/(t+100)

But when using t = 100, I get the answer to be 1501 ppb instead of the more appropriate 4.25 ppb. Where did I go wrong?