Edexcel C3 2007 June — Question 8

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
Year2007
SessionJune
TopicExponential Functions

8. The amount of a certain type of drug in the bloodstream \(t\) hours after it has been taken is given by the formula $$x = D \mathrm { e } ^ { - \frac { 1 } { 8 } t } ,$$ where \(x\) is the amount of the drug in the bloodstream in milligrams and \(D\) is the dose given in milligrams. A dose of 10 mg of the drug is given.
  1. Find the amount of the drug in the bloodstream 5 hours after the dose is given. Give your answer in mg to 3 decimal places. A second dose of 10 mg is given after 5 hours.
  2. Show that the amount of the drug in the bloodstream 1 hour after the second dose is 13.549 mg to 3 decimal places. No more doses of the drug are given. At time \(T\) hours after the second dose is given, the amount of the drug in the bloodstream is 3 mg .
  3. Find the value of \(T\).