2025 JVSS PRELIMS P2 Q3

A radioactive substance decays according to the equation \(A=15e^{-bt}\), where \(A\) is the mass in grams of radioactive substance remaining and \(t\) is the time in hours after the radioactive substance starts to decay.

1. Given that there are 10 grams of radioactive substance remaining after 30 hours, verify that the value of \(b\) is 0.013516.[2]
2. Find the mass of radioactive substance left at the end of 1 week.[1]
3. Find the number of hours for the radioactive substance to decay to half of its original mass.[3]
4. Find the rate at which the substance decays at \(t=50\) hours.[2]