Final answer:
After 12 hours, approximately 31.6% of the original drug dose remains in the bloodstream. After 48 hours, only about 1.56% of the initial dose remains. This is calculated using the formula for exponential decay based on the drug's half-life of 9 hours.
Step-by-step explanation:
The half-life of a drug refers to the time it takes for half of a dose of the drug to be eliminated from the bloodstream. In the given question, the half-life of the drug is 9 hours. To calculate the fraction of the original drug dose remaining after a certain number of hours, you can use the formula for exponential decay.
Amount remaining = Initial amount × (½)^(Time elapsed / Half-life)
In 12 hours, which is 1.333 half-lives (12/9), the fraction of the original dose remaining in the bloodstream would be:
Amount remaining = Initial amount × (½)^(12/9) × (½)^(1.333) = Initial amount × 0.316
So approximately 31.6% of the original dose would remain after 12 hours.
For 48 hours, which is 5.333 half-lives (48/9), the fraction of the original dose remaining would be approximately:
Amount remaining = Initial amount × (½)^(48/9) = Initial amount × 0.316
So, after 48 hours, a mere 1.56% of the original dose would remain in the bloodstream.