A drug is eliminated from the body through urine. Suppose that for an initial dose of 10 milligrams, the amount A (t) in the body t hours later is given by A(t) = 10(0.8) t
a) Estimate the amount of the drug in the body 8 hours after the initial dose.
b) What percent of the drug still in the body is eliminated each hour? Explain
a) To estimate the amount of the drug in the body 8 hours after the initial dose, we can substitute t = 8 into the given equation A(t) = 10(0.8)^t:
A(8) = 10(0.8)^8 = 10(0.16777216) ≈ 1.678 mg (rounded to three decimal places)
Therefore, the estimated amount of the drug in the body 8 hours after the initial dose is approximately 1.678 mg.
b) To determine the percentage of the drug still in the body that is eliminated each hour, we need to calculate the fraction remaining each hour.
Let's consider the amount of the drug remaining after 1 hour, A(1):
A(1) = 10(0.8)^1 = 8 mg
The fraction remaining after 1 hour is calculated by dividing the amount remaining by the initial dose:
Fraction remaining after 1 hour = A(1) / Initial Dose = 8 mg / 10 mg = 0.8
Similarly, we can calculate the fraction remaining after 2 hours, 3 hours, and so on.
After 2 hours, Fraction remaining = 0.8 * 0.8 = 0.64
After 3 hours, Fraction remaining = 0.8 * 0.8 * 0.8 = 0.512
After 4 hours, Fraction remaining = 0.8 * 0.8 * 0.8 * 0.8 = 0.4096
And so on...
From the pattern, we observe that for every hour the drug remains in the body, the fraction remaining reduces by a factor of 0.8. This means that 80% of the remaining drug is eliminated each hour.
Therefore, the percentage of the drug still in the body that is eliminated each hour is 80%.