Thread: Half Life-- Differential Equation-- Decay Question!

For an operation a dog is anesthetized with sodium pentobarbitol, which is eliminated exponentially from the blood stream. Assume that of any sodium pentobarbitol in the blood stream, half is eliminated in 5 hours. Assume also that to anesthetize a dog, 20 milligrams of sodium pentobarbitol are required for each kilogram of body weight. What single does of sodium pentobarbitol would be required to anesthetize a dog weighing 10 kilograms for half an hour?

Half an hour is (1/2)/5= 1/10 of the "half life" period. If the initial dose is "A", what will be left after that time? Set that equal to 20(10)= 200 milligrams and solve for A.