A hospital patient receives intravenously 16 units of a certain drug per hour. The drug is eliminated exponentially, so that the fraction that remains in the patients body for t hours is $f ( t ) = e ^ { - t / 11 }$ . If the treatment is continued indefinitely, approximately how many units of the drug will be in the patient's body in the long run? Round to two decimal places, if necessary.
A) 1.45 units
B) 176 units
C) 27 units
D) 160 units

Question

Quizplus · Accepted Answer

The steady-state amount of the drug in the body is given by the formula: $\text{Rate of infusion} \times \text{Mean residence time}$. The mean residence time is the reciprocal of the elimination rate constant, which is 11 hours in this case. Therefore, the steady-state amount is $16 \times 11 = 176$ units.

A Hospital Patient Receives Intravenously 16 Units of a Certain f(t)=e−t/11f ( t ) = e ^ { - t / 11 }f(t)=e−t/11

A Hospital Patient Receives Intravenously 16 Units of a Certain $f ( t ) = e ^ { - t / 11 }$