Question

4. 15 marks) Let C denote the concentration of paracetamol in your blood. When you take the parac- etamol C goes up quickly and then declines slowly over the next few hours, as your liver clears the drug from your body (or as the drug gets metabolised or excreted) Here are some typical data.1 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 much more quickly than the reference form. Test drg -Reference drug 9 10 12 Time (h) Suppose you take a paracetamol tablet at t 0. A reasonable model for C is 0, t < 0, COC 20, where t denotes time (in units of hours), and where Co and k are both positive constants. (a) Plot C(t). Pick values for k and Co that give you a picture that looks at least approx imately like the data. Note that the plot has to be done properly on the computer, with proper labels. (b) If C has units of ug/mL, what are the units of k and Co? (c) According to the model, what is the concentration of the drug at tmet 0? (d) At what time is the drug at half its initial concentration (i.e., half of C(0))? (e) (Challenge part. This is more difficult.) Suppose you take a second pill att 14 hours. How would you write C(t) to take this into account?

Answer 1

14 13 12 10 U T Time(h)

here equation of above plot:

clearly, C_o = 8.3 and K=0.35

(b)

Since C₀ has same unit as C.

So, unit of C₀ : $\mu g/mL$

since quantity under exponential must be dmensionless.

so K has a unit of time inverse.

So, unit of k : hour^-1

(c) Since,

$C(0)= C_0 = 8.3 \mu g/mL$

(d)

let at t=t' , C(t')= C_o/2

again from,

$t' = \frac{0.693}{0.35}= 1.98 hrs$