2024 ACS(BR) P2 Q2

The number, \(v\), of a certain virus present in a sample collected by a vaccine laboratory is given by \(v=m\mathrm{e}^{2t}+n\), where \(m\) and \(n\) are constants and \(t\) is measured in days. Initially, the number of virus present was \(2000\). It increased to \(5000\) after \(1\) day.

1. Find the value of \(m\) and of \(n\).[4]
2. Find the number of days in which the number of virus present first reach \(1\) million.[2]