SOLUTION: 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 medi

Question 1032365: 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 4 hour period.
(b) Find a formula for f in the form A � B^t
, or an equivalent form.
(c) Let Th (h is just a little below T , i cant put it in the correct form here ) be the time taken for the quantity of medicine in the bloodstream to halve. Determine
the value of th.
(d) Show that the halving time is constant.
(e) Sketch a graph of the function over a 4 hour period since the injection.
(f) 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 medical safety, should we round up or down to the nearest hour?
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Loss of 25% every 40 minutes is the same as KEEPING 75% every 40 minutes.

You are interested among other questions, in the half-life, and you can use
as the exponent. NOW, uses t to count MINUTES, so the form of the
equation is a little different. Half life would be like so...

Choosing natural log,

-------------half life in minutes.

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