The amount of medicine remaining in a patient’s bloodstream \(t\) hours after it is taken is \(M\) mg. It is modelled by the equation \(\ln\left(\dfrac M5\right)=\ln16-\dfrac t3\ln2\).
Show that the model can be written in the form \(M=80\mathrm e^{-\frac t3\ln2}\).[2]
Find the time taken for the medicine to decrease to 20 mg.[3]
A second dose should be taken only when the amount of medicine remaining in the bloodstream has fallen to less than 15 mg.
A patient takes the medicine at 07 00. The patient asks whether the second dose can be taken at 14 20.
Use the model to determine whether the second dose can be taken at 14 20. Give a reason for your answer.[3]