Drug concentration and the timing of a second dose
Drug concentration and the timing of a second dose
IP 4
10 marks
After a dose of a drug, its concentration in a patient's blood, \(C\) mg per litre, is modelled by \(C=\dfrac{20t}{t^2+4}\), where \(t\) is the time in hours after the dose, \(t\ge0\).
- Show that \(\dfrac{\mathrm dC}{\mathrm dt}=\dfrac{20(4-t^2)}{(t^2+4)^2}\).[3]
- State the time interval during which the concentration is increasing, and find the greatest concentration.[2]
- The drug is effective while \(C\ge4\). Find the period during which the drug is effective.[3]
- A nurse plans to give a second dose \(6\) hours after the first. Use the model to comment on this plan, stating one assumption the model makes.[2]
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.
Create a free account to practise similar questions.
Answer:(a) shown (b) increasing for \(0\le t\lt 2\); greatest concentration \(5\) mg per litre (c) \(1\le t\le4\) (d) the drug is ineffective from \(t=4\) to \(t=6\), so the second dose should be given at about \(t=4\); the model assumes the same clearance throughout
Need help? Join our IP Math tuition programme.
Learn more