A patient’s total cholesterol level, T (t), and good cholesterol level, G(t), at t weeks after January 1, 2016, are measured in milligrams per deciliter of blood (mg/dl). The cholesterol ratio, R(t) = G(t)∕T (t), is used to gauge the safety of a patient’s cholesterol, with risk of cholesterol-related illnesses being minimized when R(t) > 1∕5 (that is, good cholesterol is at least 1∕5 of total cholesterol).
(a) Explain how it is possible for total cholesterol of the patient to increase but the cholesterol ratio to remain constant.
(b) On January 1, the patient’s total cholesterol level is 120 mg/dl and good cholesterol level is 30 mg/dl. Though R > 1∕5, the doctor prefers that the patient’s good cholesterol increase to 40 mg/dl, so prescribes a diet starting January 1 which increases good cholesterol by 1 mg/dl per week without changing the cholesterol ratio. What is the rate of change of total cholesterol the first week of the diet?