SOLUTION: The concentration of a drug in a patient's bloodstream after t hours is modeled by the formula C(t)=11(0.72)^t, where C is measured in milligrams per liter. a)What is the initial

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Question 434697: The concentration of a drug in a patient's bloodstream after t hours is modeled by the formula C(t)=11(0.72)^t, where C is measured in milligrams per liter.
a)What is the initial concentration of the drug?
b)How long does it take for the concentration to decrease to 50% of its initial level?
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
a) The initial concentration is the value when t=0:
C%280%29+=+11%280.72%29%5E0+=+11 mg/l
b) 50% of this initial value = 0.50*C(0) = 5.5
So we need to solve the following equation for t:
5.5+=+11%280.72%29%5Et -> 0.5+=+0.72%5Et
Take the logarithm of both sides:
log%280.5%29+=+t+log%280.72%29
This gives
t+=+log%280.5%29%2Flog%280.72%29+=+2.110 hours