A patient is given an injection of 21 units of a certain drug every 24 hours.The drug is eliminated exponentially so that the fraction that remains in the patient's body after t days is $f ( t ) = e ^ { - t / 5 }$ If the treatment is continued indefinitely,approximately how many units of the drug will eventually be in the patient's body just prior to an injection?
A)94.85 units
B)46.65 units
C)115.85 units
D)141.50 units

Question

Quizplus · Accepted Answer

The steady-state amount of the drug in the body just before an injection can be calculated using the formula for the sum of an infinite geometric series. The amount remaining from each dose is a geometric series with a common ratio of $e^{-1/5}$. The sum is $S = \frac{21}{1 - e^{-1/5}}$, which approximates to 94.85 units.

A Patient Is Given an Injection of 21 Units of a Certain