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# Write down the general solution to the differential equation above.

INSTRUCTIONS TO CANDIDATES

This assignment is worth 5% of your final assessment for this course. Your answers should be well written, neat, thoughtful, mathematically concise, and a pleasure to read. Please cite any resources used and show all working. Present your arguments clearly using words of explanation and diagrams where relevant. After all, mathematics is about communicating your ideas. This is a worthwhile skill which takes time and effort to master. The marker will give you feedback and allocate an overall letter grade and mark to your assignment using the following criteria:

This assignment contains only one question.

Modelling drug decay

1. The amount of a particular drug Q(t) (measured in milligrams) at time t (measured in dQ  hours) can be modelled using the differential equation relative decay rate.

dt  = −kQ, where k > 0 is the

(a) Write down the general solution to the differential equation above.

(b) If after 10 hours, the amount of drug remaining is one fifth of the initial amount, find k. Give your answer in exact form.

(c) What is the half-life of this drug?

(d) It is important that the level of drug does not drop below 5 mg. Also, it is unsafe to give another dose of the drug if there is more than 12 mg remaining. If the initial dose of the drug is 30 mg, calculate the time interval in which it is safe to give the next dose of the drug, after the patient receives the initial dose.

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