The glucose test

A hospital checks a patient for diabetes mellitus with a glucose test. The fasting level and the level two hours after a drink of 75 g of glucose are compared with two cut-offs. You will also write the teaching model of the lesson.

The idea. A person meets the criteria when the fasting level is 126 mg/dL or more, or the two hour level is 200 mg/dL or more. One mmol/L is 18 mg/dL.

Your tasks.

1. Finish to_mgdl. It changes mmol/L to mg/dL.
2. Finish diabetes. It gives True when either cut-off is reached.
3. Finish glucose. Let r be the response of the cells to insulin, where 1 is normal. The fasting level is $90 + 50(1 - r)$ mg/dL. The time of the peak is $t_p = 45 + 100(1 - r)$ minutes. The rise at the peak is $50 + 100(1 - r)$ mg/dL. The level at time t is the fasting level plus the rise times $\dfrac{t}{t_p} e^{1 - t/t_p}$.