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.
- 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.
- 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 .
- Find the value of \(T\).