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A 13yr old girl is brought to the emergency department by her father after he found her in semicomatose state with an empty bottle of antihistamine beside her bed. plasma diphenhydramine concentrations measured hourly for 6hr are shown.

Time plasma drug concentration (ng/ml)
1:00pm 240
2:00pm 202
3:00pm 170
4:00pm 143
5:00pm 120
6:00pm 101

Approximately how long after the first measurement(in hours)will take for this patient's plasma concentration to drop below 10ng/ml?

a.10
b.12
c.16
d.20
e.24
f. 30
g.38
 

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D - 20? I'm not 100% so maybe someone can verify but here's my method:

To get to half the original concentration, it took from 1pm to 5pm = ie: 4hrs

We need the concentration to drop below 10

so, our calculation is as follows:

240 - 120 - 60 - 30 - 15 - 7.5

ie each dash is 4 hours long assuming this is first order kinetics

and since there are 5 dashes - 5 X 4 = 20 hours...
 

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i think the answer is d:) 20 hours
i solved it this way : at 5 pm, the concentration of the drug is half the original concentration, which means that the half life of this drug is from 1 pm to 5 pm which is 4 hours ... a 240 ng/ml needs 5 half lives to get below 10 ( 7.5 ng/dl exactly ) and this would be 5 half lives times 4 hours each = 20 hours ... i hope this solution will be correct and useful
 

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it is d

its easy
T half is the time needed for plasma concentration of drug to decrease by half

and her plasma conc of the drug was 240 at 1 pm and reach half at5 pm
so t half = 4 hours

after 1st t half 120
after 2nd thalf 60
after 3rd thalf 30
after 4th thalf 15
after 5th thalf 7.5

so it decrease below 10 ng after 5 thalf
so after 20 hours
so it is d for sure
 
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