Question 1196944
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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: <font color=red>8 hours</font>


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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: <font color=red>Approximately 14.768 mg/mL</font>
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