2026 HGV P2 Q7

A medical experiment was conducted on a group of 200 adults suffering from migraine. They were each administered different amounts of medicine and the time taken for the medicine to take effect was recorded. The time taken, \(t\) hours, for \(x\) milligrams of medicine to take effect is given by \(t=\dfrac{10}{e^{0.5x}}\) where \(1\le t\le12\).

1. Find the least amount of medicine required to take effect in 30 minutes.[3]
2. How long does it take for 8 milligrams of medicine to take effect?[2]