Question

The half-life of a medication prescribed by a doctor is 6 hours. How many mg of this medication is left after 78 hours if the doctor prescribed 100 mg?

Answer 1

0.195

Explanation:

The half-life of the medication is 6 hours, which means that every 6 hours the amount of medication is reduced by half.

After 6 hours, the amount of medication left is 50mg (half of 100mg).

After another 6 hours (12 hours total), the amount of medication left is 25mg (half of 50mg).

After another 6 hours (18 hours total), the amount of medication left is 12.5mg (half of 25mg).

This pattern continues until the 78th hour, which is 13 half-lives (78/6 = 13).

So, the amount of medication left after 78 hours is:

100 mg ÷ 2^13 = 0.1953125 mg (rounded to 3 decimal places)

Therefore, approximately 0.195 mg of medication is left after 78 hours.