Answer:
The amount of drug left in his body at 7:00 pm is 315.7 mg.
Explanation:
First, we need to find the amount of drug in the body at 90 min by using the exponential decay equation:
[tex] N_{t} = N_{0}e^{-\lambda t} [/tex]
Where:
λ: is the decay constant = [tex]ln(2)/t_{1/2}[/tex]
[tex]t_{1/2}[/tex]: is the half-life of the drug = 3.5 h
N(t): is the quantity of the drug at time t
N₀: is the initial quantity
After 90 min and before he takes the other 200 mg pill, we have:
[tex]N_{t} = 200e^{-\frac{ln(2)}{3.5 h}*90 min*\frac{1 h}{60 min}} = 148.6 mg[/tex]
Now, at 7:00 pm we have:
[tex]t = 7:00 pm - (5:00 pm + 90 min) = 30 min[/tex]
[tex]N_{t} = (200 + 148.6)e^{-\frac{ln(2)}{3.5 h}*30 min*\frac{1 h}{60 min}} = 315.7 mg[/tex]
Therefore, the amount of drug left in his body at 7:00 pm is 315.7 mg (from an initial amount of 400 mg).
I hope it helps you!
