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? Round your answer to the nearest hundredth, and do not include units​

Answer 1

Using the exponential decay formula, we can find the half-life of the medication from the initial and given 8-hour amounts and then use it to calculate the amount of medication remaining after 10 hours.

Step-by-step explanation:

To determine the remaining medication after a given number of hours, we will apply the exponential decay formula which accounts for substances with a half-life. Thus, given that there are initially 20 milligrams of the medication and that it decreases to 12 milligrams after 8 hours, we need to calculate the half-life and then use it to predict the amount remaining after 10 hours.

First, finding the half-life 't1/2' can be done using the formula A = A0×2−t/t1/2, where A is the remaining amount (12 mg), A0 is the initial amount (20 mg), and t is the time elapsed (8 hours). Solving for the half-life gives us t1/2 as the unknown in this equation.

12 mg = 20 mg ×2−(8 hours)/t1/2
Reducing this equation, we find that:
t1/2 = 8 hours / (log2(20 mg/12 mg))

After finding 't1/2', we can then determine the amount remaining after 10 hours. The calculation would be as follows:
A = 20 mg ×2−(10 hours)/t1/2

This will give us the final amount of medication left in the system at the 10-hour mark, rounded to the nearest hundredth.

Answer 2

At 10 hours there will be 10 milligrams

Step-by-step explanation:

On a graph your slope would be y= -1x+20 because there where 20 mill at 0 hours and 12 mill at 8 hours. 20-8=12 meaning 1 mill would be deluded every hour. Hope this helps.