The presence of toxins in a certain medium destroys a strain of bacteria at a rate jointly proportional to the number of bacteria present and to the amount of toxin. If there were no toxins present, the bacteria would grow at a rate proportional to the amount present. Let x denote the number of living bacteria present at time t. Assume that the amount of toxin is increasing at a constant rate and that the production of the toxin begins at time t = 0. Set up a differential equation for x. Solve the differential equation.
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