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1. A drug is injected in to a region of muscle that has a volume of 0.33 liters.

ID: 931903 • Letter: 1

Question

1. A drug is injected in to a region of muscle that has a volume of 0.33 liters. The muscle is well supplies with blood and the drug is removed from the muscle at a rate that is proportional to the drug concentration. a) Write down the differential equation that describes the drug concentration as a function of time d[c]/dt=? b) Solve the differential equation from (a) subject to the boundary condition that the drug at t=0 is given C0 and given that the half life for the drug concentration in the muscle is 3 hrs. c) If C0=22 mg/liter, find C after 2 hrs. d) If the therapeutic range of the drug is 30 mg/l> C >18 mg/l, determine effective drug dose that requires the fewest possible injections. e) Determine the rate of continuous injection (IV) that would maintain the optimal dose of 22 mg/l at al times.

2. A leaky drum of toxic chemical X is dumped in to a river. The diffusion constant for chemical X in water is 3X10-9 m2/s. a) If the river is flowing at 0.2 m/s and you are bathing 50 m upstream, do you expect the toxic chemical to reach you? b) What is the slowest current velocity that would make it safe to bath 5 m upstream of the barrel?

Explanation / Answer

1. A drug is injected in to a region of muscle that has a volume of 0.33 liters.