It will take approximately 37.45 days for 95% of the original dose to be eliminated from the body of an average adult patient, assuming exponential behavior for the elimination.
The Half-Life of a drug given to an average adult is 3 days. It is necessary to determine the time required for 95% of the original dosage to be removed from the body of an average adult patient by using the following information:
Half-Life = 3 days
The formula to calculate the time taken for a drug to be eliminated is:
Time = Half-Life × 2n
Where n is the number of half-lives completed by the drug.
Exponential behavior of the elimination of the drug is assumed. When 95% of the original dose has been eliminated from the body, only 5% of the original dose remains.
To find the number of half-lives, use the following formula:
Remainder = Original Amount × (1/2)²n
Where,
Remainder = 0.05
(as 95% of the original dose has been eliminated)
Original Amount = 1
(100% of the original dose)
Now substitute the values in the above formula
0.05 = 1 × (1/2)²n
Solving this equation for n:
n = 4.32 half-lives
To find out the time required for 95% of the original dose to be eliminated from the body of an average adult patient, substitute the value of n in the formula for time:
Time = Half-Life × 2n
Time = 3 days × 24.32
= 37.45 days
Hence, it will take approximately 37.45 days for 95% of the original dose to be eliminated from the body of an average adult patient, assuming exponential behavior for the elimination.
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