Differential Equation - Word problem about toxic levels in a body

Hey MHF gang,

I need some assistance on a Calculus project I am working on. It is a problem that is centered around the concept of differential equations, so hopefully someone can help me.

I won’t go into all of the details of the project, but I need some initial help setting up the differential equation, and I can go from there. I’m not sure if what I have is correct, so I’m looking for a second opinion.

**Here is the relevant data:**

Basically, toxic has been entering a man’s body for 6 months.

Per day, 795 mg (0.00795 grams) of toxic is entered into a body.

15% is absorbed into the blood. From the blood, 0.39% of toxic gets into the bones per day, and 3.22 of toxic is excreted out of the body per day.

Initially, the man has no toxic in his body. After 6 months, he has 60 mg/dL (or about .35 grams).

A clue that is given is “change in bone level is the blood level; change in blood level is intake minus output”. The amount of toxic in bones is what determines how deadly the amount is.

What I know is that dy/dt = (toxic rate in) – (toxic rate out). I have formed what I think is the correct DFE, but I want to see if you guys come up with the same thing. What throws me off is not knowing how much blood the body has overall...

This is somewhat urgent, so please help as soon as you can. Thanks for reading!

- Taichi Chunami