Question 1196944: The remaining concentration of a drug in a person’s bloodstream is modeled by the relation C=C0(1/2)^t/8, where C is the remaining concentration of the drug in the bloodstream in milligrams per milliliter of blood, C0 is the initial concentration, and t is the time, in hours, that the drug is in the bloodstream.
What is the half-life of this drug?
A nurse gave a patient this drug, which was 20 mg/ml. What is the concentration of this drug in 3.5 hours?
Found 2 solutions by math_tutor2020, josgarithmetic:
Answer by math_tutor2020(3816)   (Show Source):
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Part A) What is the half-life of this drug?
There are a few ways to write a half-life formula
One such way is to write it like this
y = a*(1/2)^(t/H)
the variables are
a = initial amount
H = half-life
t = number of time units
y = amount remaining after t time units elapsed
We see that H = 8 is the half life.
Every 8 hours, the drug concentration in the bloodstream will cut in half.
Answer: 8 hours
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Part B) A nurse gave a patient this drug, which was 20 mg/ml.
What is the concentration of this drug in 3.5 hours?
We have a = 20 mg per mL as the initial concentration.
In other words, for each mL of blood, the patient gets 20 mg of the drug.
This will replace the C0 in the equation C=C0(1/2)^(t/8) since C0 takes the role of 'a' which is the initial value.
So we have C=20(1/2)^(t/8)
Now let's determine C when t = 3.5 hours
C=20(1/2)^(t/8)
C=20(1/2)^(3.5/8)
C=14.768261459395
C=14.768
Round this value however needed, or however your teacher instructs.
Answer: Approximately 14.768 mg/mL
Answer by josgarithmetic(39616) (Show Source):
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