Final answer:
The concentration of the drug after 165 minutes, which corresponds to 5 half-lives, is calculated as 0.047 ug/mL when rounded to two significant digits, based on the initial concentration and first-order elimination kinetics.
Step-by-step explanation:
The rate at which a certain drug is eliminated by the body following first-order kinetics with a half-life of 33 minutes implies that the concentration halves every 33 minutes. The question asks what the concentration will be 165 minutes later if we start with 1.5 ug/mL. To calculate this, we can use the first-order kinetics formula or simply recognize that 165 minutes is equal to 5 half-lives (165/33 = 5).
Using the formula for the amount remaining after n half-lives for a first-order reaction, which is:
Amount remaining = Initial amount × (1/2)^n
Where n is the number of half-lives.
We can substitute the given values into this equation:
Amount remaining = 1.5 ug/mL × (1/2)^5
Amount remaining = 1.5 ug/mL × 1/32
Amount remaining = 0.046875 ug/mL
Rounded to two significant digits, the amount remaining is 0.047 ug/mL.