a diabetic patient takes 1500 milligrams of metformin each day. it is excreted from the body at a rate proportional to the amount present, with constant of proportionality equal to 0.9 (with time in days). that is, it is eliminated at a rate of 90% per day. write a differential equation modeling the amount of metformin m in the patient’s body at time t in days.
use euler’s method on the differential equation from 1 to predict the amount of metformin in a patient’s body over time with initial amount equal to 0 mg: ?
a. during the first 5 days of treatment with a step-size of h=1 day
b. during the first 2 days of treatment with a step-size of h=0.5 days
2. consider the differential equation from 1 and your answers to 3.
a. what is happening to the amount of metformin in the patient’s body over time?
b. when is the rate of change of the metformin equal to zero?
c. when is the rate of change of the metformin greater than zero?
d. when is the rate of change of the metformin less than zero?
e. summarize your results from parts (). that is, what will happen to the amount of metformin in the body for initial amounts in the range of [0,3000] milligrams?