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The speed with which a drug spreads in the bloodstream is governed by the differential equation,...

The speed with which a drug spreads in the bloodstream is governed by the differential equation, dX/dt=a-bX where a and b are positive constants. The function X (t) describes the amount of the drug in the bloodstream at an instant t. Find the limit value of X (t) when t goes to infinity. How long does the concentration of the drug take to reach half of this limit concentration? Assume that at time t = 0 the amount of the drug in the blood is zero.

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