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

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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(39838) About Me  (Show Source):
You can put this solution on YOUR website!
"At noon an injection..." gives the data to find k in the first equation.
C%2FCo=e%5E%28-kt%29
ln%28C%2FCo%29=-kt%2Aln%28e%29
ln%28C%2FCo%29=-kt
k=-%281%2Ft%29ln%28C%2FCo%29
highlight_green%28k=%281%2Ft%29ln%28Co%2FC%29%29
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 k=%281%2F3%29ln%282%29.
highlight_green%28k=0.231%29.

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 T=%281%2Fk%29ln%285%29,
T=%281%2F0.231%29ln%285%29
highlight%28T=6.97%29, not sure if to the nearest hour might be best or not; but this could be stated T is 6 hours and 58 minutes.