Question 898295: How to use the C(t) = Co e ^(-rt) formula?
Here is some background information
Exponential functions can be used to model the concentration of a drug in a patient's body. Suppose the concentration of Drug X in a patient's bloodstream is modeled by,
C (t) = C0 e - rt,
where C (t) represents the concentration at time t (in hours), C0 is the concentration of the drug in the blood immediately after injection, and r > 0 is a constant indicating the removal of the drug by the body through metabolism and/or excretion. The rate constant r has units of 1/time (1/hr). It is important to note that this model assumes that the blood concentration of the drug (C0 ) peaks immediately when the drug is injected.
the problem says
Round your answer to the nearest tenth and use the model C(t) = Co e^(-rt). If for drug x, r = 0.20 1/hr
a) how long after injection does it take for the concentration of a drug x to decrease to 35% of the initial level?
b) what can be said about the drug concentration in the body and the removal rate for this scenario. Use units of measure.
Any help would be really appreciated. I am very stuck on this problem
thank you
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Round your answer to the nearest tenth and use the model C(t) = Co e^(-rt). If for drug x, r = 0.20 1/hr
a) how long after injection does it take for the concentration of a drug x to decrease to 35% of the initial level?
C(t) = Co e^(-rt)
0.35 = e^(-0.2t)
ln(0.35) = -0.2t
t = -ln(0.35)/0.2
t =~ 5.25 hours
--> 5.3 hours
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b) what can be said about the drug concentration in the body and the removal rate for this scenario. Use units of measure.
The removal rate is dependent on the amount remaining, ie, the concentration.
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