For a nonsmoker, the biological half-life of theophylline is 8 hours. Find the amount of the drug retained in a nonsmoker's system 18 hours after taking a one-unit dose. (Round your answer to three decimal places.)
18 / 8 = 2.25 half lives
1 unit *(1/2)^2.25 = .210 unit left
To find the amount of theophylline retained in a nonsmoker's system 18 hours after taking a one-unit dose, we can use the formula:
Amount retained = initial dose * (1/2)^(t/h)
Where:
- initial dose is the amount initially taken
- t is the elapsed time since the initial dose
- h is the biological half-life of the drug
In this case, the initial dose is one unit, t is 18 hours, and the biological half-life is 8 hours.
Amount retained = 1 * (1/2)^(18/8)
To calculate this expression, let's substitute the values and calculate:
Amount retained = 1 * (1/2)^(2.25)
To evaluate (1/2)^(2.25), we can use a calculator:
Amount retained ≈ 0.396
Therefore, the amount of theophylline retained in a nonsmoker's system 18 hours after taking a one-unit dose is approximately 0.396 units.
To find the amount of theophylline retained in a nonsmoker's system 18 hours after taking a one-unit dose, we can use the formula for exponential decay:
A = A₀ * (1/2)^(t / h)
Where:
A is the current amount of the drug in the system
A₀ is the initial amount of the drug
t is the time that has passed
h is the biological half-life of the drug
In this case, A₀ is the one-unit dose (which we don't know yet), t is 18 hours, and h is 8 hours.
We can rearrange the formula to find A₀:
A = A₀ * (1/2)^(t / h)
A₀ = A / (1/2)^(t / h)
Now we can plug in the given values:
t = 18 hours,
h = 8 hours,
A = ?
A₀ = A / (1/2)^(18 / 8)
Let's calculate this expression:
A₀ = A / (1/2)^(2.25)
A₀ = A / 0.353553
Now, since A₀ is the initial amount of the drug, which is a one-unit dose, we have A₀ = 1.
1 = A / 0.353553
To find A, we can rearrange the equation:
A = 1 * 0.353553
A = 0.353553
Therefore, the amount of theophylline retained in a nonsmoker's system 18 hours after taking a one-unit dose is approximately 0.354 (rounded to three decimal places).