I'm giving that a child has swallowed 11 pills of 100 milligrams of a drug and was rushed into the emergency room after 2 hours by that time the drugs have passed from his stomach to his intestines.
The drug is absorbed in the blood steam at a proportional rate to the quantity in the digestive system,and the drug is removed from the blood at a proportional rate to the quantity that is in the blood.
(**)
It is known there is half-life for 5-hour blood absorption and half-life for removal from the blood (The time when the amount of the drug decreases by half in the blood,assuming there is no any drug absorbtion) is 6 Hours.
I'm trying to write a differential equation for the quantity of the drug in the digestive system and an equation of the quantity of the drug in the blood both equations are by time and with a starting condition.
I'm having trouble understanding (**) to write my first equation ,i'm trying to understand by how much time the quantity of the drug gets absorbed by the digestive system and delivered to the bloodstream to build my first equation.
From the given i can say that
G(0)=1,100 (the quantity of the drug in the digestive system at the initial time is 1,100 milligrams)
Best Answer
You get as equations \begin{align} \dot G &= -k_1G\\ \dot L &= k_1G-k_2L \end{align} and from the half-life times $e^{-5k_1}=0.5$ and $e^{-6k_2}=0.5$, where time is measured in hours.