SOLUTION: 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

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): You can put this solution on YOUR website!

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

--------------------------------------------------------------------------------------

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(39617) (Show Source): You can put this solution on YOUR website!
duplicate
RELATED QUESTIONS
The remaining concentration of a drug in a person’s bloodstream is modeled by the... (answered by Theo)
A drug is injected into a patient and the concentration of the drug in the bloodstream is (answered by math33)
Ok so I have an exponential and log functions activity and I am stuck on 1 problem. I... (answered by josgarithmetic)
Drug Concentration. When a pharmaceutical drug is injected into the bloodstream, it's... (answered by josgarithmetic)
How to use the C(t) = Co e ^(-rt) formula? Here is some background information... (answered by Alan3354)
The concentration of a drug in a bloodstream, measured in milligrams per liter, can be... (answered by Fombitz,Boreal)
The concentration of a drug in a patient's bloodstream after t hours is modeled by the... (answered by htmentor)
A drug is administered to a patient and the concentration of the drug in the bloodstream... (answered by jim_thompson5910)
Please help me solve this equation: A drug is administered to a patient and the... (answered by Boreal)

SOLUTION: 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

SOLUTION: 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