(Pharmacokinetics Application) A certain medicine is eliminated from the bloodstream…

MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

(Pharmacokinetics Application) A certain medicine is eliminated from the bloodstream according to the exponential model

C(t)=C_0 e^{-\lambda t}

, where

C(t)

(in mg) is the concentration at time

t

hours after administration. A patient is given a single dose resulting in an initial blood concentration of

200\,\text{mg}

. After

8\,\text{h}

the concentration is measured to be

50\,\text{mg}

. (i) Determine the decay constant

\lambda

of the medicine, correct to four decimal places. (ii) Calculate the half-life of the medicine in the patient’s bloodstream. (iii) Find the time after administration when the concentration will first fall below

5\,\text{mg}

. Give your answer to the nearest tenth of an hour. (iv) The medicine is considered safe for a repeat dose only when the concentration has fallen below

25\,\text{mg}

. Comment, with justification, on whether a second identical dose may be safely administered

12\,\text{h}

after the first dose.

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