When doctors prescribe medication, they give patients instructions as to how much to take and how often it should be taken. The amount of medication in your body varies with time. Suppose the equation
M(t) = 0.5t4 +3.5t3 – 100t2 + 350t models the number of milligrams of a certain medication in the
bloodstream + hours after it has been taken. The doctor can use roots of this equation to determine how
often the patient should take the medication to maintain a certain concentration in the body.
a. How often should a patient take this medication?
b. If the patient took the medicine at 8 am, at what time will the medicine be at its highest amount of
concentration in his bloodstream?