*Image courtesy of Adam Hart-Davis/DHD Gallery*

Cardizem^{tm} is used in treating the symptoms of chronic angina and hypertension. As a calcium channel blocker, it is
able to both increase the myocardial oxygen supply and decrease the body's demand for oxygen.
It does this by lowering the heart rate and expanding the volume of the circulatory system,
which leads to a lower blood pressure.
Experiments show that the drug Cardizem^{tm} (diltiazem hydrochloride)
has a half life of 20 hours inside the human body. In our model the rate of change of Cardizem^{tm}
in the body is assumed to be proportional to the amount present.

**Problem 1:** Write a differential
equation describing the rate of change of the quantity of Cardizem^{tm}
and determine the constant of proportionality.

**Problem 2:** Old man Withers receives
Cardizem^{tm} intravenously at a continuous rate of 4 mg/min.
Write a differential equation describing the rate of change of the quantity
of Cardizem^{tm} and compute its solution assuming that there is
no Cardizem^{tm} initially present in old man Withers.

**Problem 3:** The fluid in the IV bag
is emptied in two hours. How much Cardizem^{tm} is in old man Withers's
blood stream at that point?

**Problem 4:** Two hours after the bag
is emptied, a nurse realizes he has forgotten to replace the bag. To make
up for lost time, he triples the rate at which Cardizem^{tm} is
administered. He then puts up a larger bag that can feed Cardizem^{tm} at this faster rate for up to 6 hours.
He also leaves a note for the next nurse to turn down the rate of flow,
but the note is swept off the counter by a breeze from the door after he
leaves. The next nurse doesn't notice the note lying on the floor, so she
doesn't check the rate of flow.

The lethal amount of Cardizem^{tm} is 40 mg per kg of body mass. Determine if
old man Withers will become old dead man Withers if he weighs 100 kg.

** Hint**: What differential equation describes the rate of change
of Cardizem

^{tm}during the 2 hours without an IV? What about after the new IV is administered? It is helpful to take t=0 to be the initial time for each new differential equation and determine the quantity of Cardizem

^{tm}using the previous solution. Also take care to be consistent with your units of measure.

With the advent of HTML5, Javascript is now ready for prime time
for mathematical applications. There are
new Javascript demos
illustrating how we might use interactive web objects to
help students learn Calculus.