Question 1077994: Suppose the quantity Q, in mg, of medicine in a patient’s bloodstream is decreasing by 25% each
40 minutes. Let us write Q = f(t), where t is in minutes since the injection of medicine. Suppose
the injection contains 300 mg of medicine.
(a) Construct a table of values for Q as a function of t over a few hours.
(b) Find a formula for f in the form A × B^t
, or an equivalent form.
(c) Let th be the time taken for the quantity of medicine in the bloodstream to halve. By a process
of guessing and checking, estimate the value of th (accurate to 3 significant figures).
(d) Determine the exact value of th.
(e) Show that the halving time is constant. That is, show that starting from an arbitrary time
t = a, the quantity of medicine is halved after an additional time th.
(f) Sketch a graph of the function over a 4 hour period since the injection.
(g) The patient can receive a new injection when the quantity of medicine is less than 2% of the
original dose. For simplicity, this time delay is measured in a whole number of hours. Determine
the wait time. For medicinal safety, should we round up or down to the nearest hour?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620)   (Show Source):
Answer by ikleyn(52810)  (Show Source):
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