A drug is administered using intravenous infusion (IV). Assuming it can be modeled by a one...

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A drug is administered using intravenous infusion (IV). Assuming it can be modeled by a one compartment model for the amount r(t) in the plasma with elimination rate is k > 0. The drug input is given by I(t) = A, 0≤ t < 2, 0, t≥ 2. Here time is in hours. (a) Set up a differential equation for r(t) by converting I(t) to a single line function using the Heaviside step function. (b) Use Laplace transform to solve the ODE assuming x(0) = 0. Show all details. kfz(t)dt. x(t)dt. Verify (c) The total amount of drug that is removed or eliminated is equal to k that all the drug is removed. (d) Plot r(t) for 0 < t < 8 if the half-life of the drug in the blood is 5 hours, and A = 3. A drug is administered using intravenous infusion (IV). Assuming it can be modeled by a one compartment model for the amount r(t) in the plasma with elimination rate is k > 0. The drug input is given by I(t) = A, 0≤ t < 2, 0, t≥ 2. Here time is in hours. (a) Set up a differential equation for r(t) by converting I(t) to a single line function using the Heaviside step function. (b) Use Laplace transform to solve the ODE assuming x(0) = 0. Show all details. kfz(t)dt. x(t)dt. Verify (c) The total amount of drug that is removed or eliminated is equal to k that all the drug is removed. (d) Plot r(t) for 0 < t < 8 if the half-life of the drug in the blood is 5 hours, and A = 3.

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a The differential equation for xt can be set up as follows dxdt kx At2 where t2 is the Heaviside st... View the full answer