Question

A 0.3 ml dose of a drug is injected into a patient steadily for 0.35 seconds. At the end of this time, the quantity, Q, of the drug in the body starts to decay exponentially at a continuous rate of 0.4 percent per second. Using formulas, express Q as a continuous function of time, t, in seconds.

Answer 1

Hi Brittany, you're going to need a split function, one where t <= 0.35 and one where t > 0.35.

a) When t <= 0.35
The information you have is: when t = 0, the quantity will also be zero. When t = 0.35 the quantity will be 0.3. Seems like this will be a linear equation

b) When t > 0.35
The information you have that for every second that goes by Q will decrease by .4 percent. So you'll have to take away .4% of Q each t.

Make sense? Let me know if you need more help!