Question

You are given a dose of pain medication at the doctor's office. You are given 500mg. Assume that after one hour of taking it, 15% is eliminated from the body. After another hour another 15% is eliminated.

How much will be left in the body after two hours? How long until half would be left in your system?

Answer 1

Approximately 361.25mg of the medication would be left in the body after two hours. Determining the exact time until half the dose is left without the drug's half-life requires a more complex calculation, such as using logarithms or iterative methods.

Step-by-step explanation:

To calculate the amount of pain medication left in the body after two hours when an initial dose of 500mg is given and 15% is eliminated each hour, we perform two successive calculations, each reducing the remaining amount by 15%. In mathematical terms, this calculation is typically referred to as exponential decay, which can also be applied to other contexts such as radioactive decay in Physics or pharmacokinetics in Medicine.

To find out how much is left after the first hour:

• 500mg - (15% of 500mg) = 500mg - 75mg = 425mg

After the second hour:

• 425mg - (15% of 425mg) = 425mg - 63.75mg ≈ 361.25mg

So, approximately 361.25mg of the medication would be left in the body after two hours.

To find out how long it would take for half of the dose to remain, we set up an equation based on the drug's half-life knowledge:

1. 500mg * (1 - 0.15)t = 250mg
2. Solving for 't' gives the number of hours needed for half of the drug to be eliminated based on the 15% decay per hour.

Without the exact half-life, a precise solution can't be given, but we can approximate this using an iterative or logarithmic approach. In practice, this type of calculation would actually involve more complex biomedical modeling considering multiple factors influencing drug elimination rates and patient-specific variables.

Answer 2

After two hours, 361.25mg of the medication will be left in the body. Cannot determine the time until half would be left without the half-life information.

Step-by-step explanation:

To find out how much medication will be left in the body after two hours, we need to calculate the remaining amount after each hour.

After the first hour, 15% of the initial dose (500mg) is eliminated, which is 0.15 * 500mg = 75mg. So, after the first hour, 500mg - 75mg = 425mg of the medication will be left.

After the second hour, another 15% of the remaining dose (425mg) is eliminated, which is 0.15 * 425mg = 63.75mg. So, after two hours, 425mg - 63.75mg = 361.25mg of the medication will be left in the body.

The half-life of the medication is not provided, so we cannot determine exactly how long until half would be left in the system. The half-life is the time it takes for the concentration of the medication in the body to reduce by half. Without this information, we cannot calculate the time.