SOLUTION: Drug Concentration. When a pharmaceutical drug is injected into the bloodstream, it's concentration at time t can be approximated by C(t) = C0(e)^-kt, where C0 is is the concentrat

Question 898920: Drug Concentration. When a pharmaceutical drug is injected into the bloodstream, it's concentration at time t can be approximated by C(t) = C0(e)^-kt, where C0 is is the concentration at t = 0. Suppose the drug is ineffective below a concentration C1 and harmful above concentration C2. Then it can be shown that the drug should be given at intervals of the time T. Where T = (1/k)ln(C2/C1).
A certain drug is harmful at a concentration five times the concentration below which it is ineffective. At noon an injection of the drug result in a concentration of 2 mg per liter of blood. Three hours later the concentration is down to 1 mg per liter. How often should the drug be given?
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
"At noon an injection..." gives the data to find k in the first equation.

The variable choices are slightly different than yours.
The data in the rest of that sentence and the next one put into this formula makes .
.

Knowing the value for k allows you to find the value for T, the time interval between effective and harmful. Now, using YOUR choice of variables, C2=5*C and C1=C in this case for some constant C. This gives ,

, not sure if to the nearest hour might be best or not; but this could be stated T is 6 hours and 58 minutes.
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