Suppose x and y are the populations of two different species. Describe in words how each population changes with time.

A kidney removes toxins from the blood. If a kidney does not function, the toxins can be removed by dialysis. This problem explores a model for Q₁(t), the quantity of toxins in the body outside the blood, and Q₂(t), the quantity of toxins in the blood, where t is the time after dialysis started.
(a) The quantity Q₁ changes for three reasons. First, toxins are created outside the blood at a constant rate, say A. Second, toxins flow into the blood at a rate proportional to the quantity outside the blood. Third, toxins flow out of the blood at a rate proportional to the quantity in the blood. Write a differential equation for Q₁.
(b) The quantity Q₂ changes for three reasons. First, dialysis removes toxins from the blood at a rate proportional to the toxins in the blood. Second and third, the same flows into and out of the blood that change Q₁ also change Q₂. Write a differential equation for Q₂.