Therefore, it takes approximately 15.03 hours for the amount of drug in the body to reach 10% of the initial dose.
The problem involves exponential decay, where the drug amount remaining in the body decreases over time. We can model this phenomenon using the following equation:
D(t) = D₀ * (1 - r)^t
where:
`D(t)` is the amount of drug remaining in the body at time `t`
`D₀` is the initial dose of the drug
`r` is the elimination rate (as a percentage, we need to convert it to a decimal first)
`t` is the time in hours
We are given that:
`r = 15%` (converts to 0.15 as a decimal)
We want to find `t` when `D(t) = 0.1D₀` (10% of the initial dose)
Steps to solve:
1. Substitute the known values into the equation:
0.1D₀ = D₀ * (1 - 0.15)^t
2. Simplify the equation:
0.1 = (0.85)^t
3. Take the natural logarithm of both sides to solve for `t` (using the property: ln(a^b) = b*ln(a)):
ln(0.1) = t * ln(0.85)
4. Solve for `t`:
t = ln(0.1) / ln(0.85) ≈ 15.03 hours
Note: This is an idealized model and does not account for individual factors that can affect drug elimination, such as metabolism, kidney function, and body composition.
Complete the question:
A drug is eliminated from the body at a rate of 15%/hr. After how many hours does the amount of drug reach 10% of the initial dose?