Pharmacology question regarding half-life calculation

Question

A patient with chronic kidney disease has a vancomycin serum level drawn that returns at 37mcg/mL. She will require a redose when the level reaches 15mcg/mL. Her half-life has been determined to be 46 hours. How many hours after the initial serum draw will she require a redose.

 

A. 52 hours B. 60 hours C. 67 hours D. 73 hours E. 80 hours

Answer 1

Hello,

 

The formula I like to use for this. F=I x (1/2)^(t/h)

 

F is final amount 

I initial amount 

t is time to get to the final amount

h is half life 

Lets us plug in the values we have 

F is 15 mcg/ml 

I is 37 mcg/ml 

h is 46 hours 

t is what we are solving for 

 

15=37 x (1/2)^t/46.  t is what we are solving for. We must use algebra.  

 

After taking log of both sides you will end up with 

 

t=-((46(log(3)+log(5)-log(37)))/(log(2))

 

If you put this on a calculator it is 59.917 about 60 

 

Therefore answer is B.