Question

A patient takes a medication with a half life. Initially, there are 20 milligrams of the medication in the patient's system. After 8 hours there are 12 milligrams. How many milligrams will there be after 10 hours?

Answer 1

To calculate the amount of medication remaining after 10 hours, we use the half-life formula after determining the half-life based on the information that after 8 hours, the medication reduces to 12 milligrams from an initial 20 milligrams.

Step-by-step explanation:

The subject in question involves the mathematical concept of exponential decay, specifically related to the half-life of a medication. Initially, there are 20 milligrams of the medication in the patient's system, and we are given that after 8 hours, this amount has reduced to 12 milligrams. Using the half-life formula, we need to find the amount of medication left in the system after 10 hours.

To determine the number of half-lives that have passed in 8 hours, we use the formula:

• Amount remaining = Initial amount * (1/2)^(time/half-life)

Assuming the half-life (h) can be calculated as 8 hours / number of half-lives = 8 / log2(20/12), we can find h and use it to determine the amount of medication left after 10 hours:

• Amount after 10 hours = 20 mg * (1/2)^(10/h)

After performing the calculations, we would obtain the exact milligram amount of medication remaining after 10 hours.