Let C denote the concentration of paracetamol in your blood.

When you take the paracetamol C goes up quickly and then declines slowly over the next few hours, as the drug gets metabolised or excreted.
Typical data are shown in Fig. 4.11

(Portolés et al, 2003). The

"test drug" and "reference drug" refer to two slightly different forms of paracetamol; the data show how the test version of the drug is absorbed more quickly than the reference form.

Suppose you take a paracetamol tablet at t = 0. A reasonable model for C is C(t) = (
0, t < 0, C0e −kt , t ≥ 0, where t denotes time (in units of hours), and where C0 and k are both positive constants.

a. Plot C(t). Pick values for k and C0 that give you a picture that looks at least approximately like the data.

b. If C has units of µg/mL, what are the units of k and C0?

c. According to the model, what is the concentration of the drug at time t = 0?

d. At what time is the drug at half its initial concentration (i.e., half of C(0))?

e. Suppose you take a second pill at t = 14 hours. How would you write C(t) to take this into account?