7 The number of micro-organisms in a population at time \(t\) is denoted by \(M\). At any time the variation in \(M\) is assumed to satisfy the differential equation $$\frac { \mathrm { d } M } { \mathrm {~d} t } = k ( \sqrt { } M ) \cos ( 0.02 t )$$ where \(k\) is a constant and \(M\) is taken to be a continuous variable. It is given that when \(t = 0 , M = 100\).

1. Solve the differential equation, obtaining a relation between \(M , k\) and \(t\).
2. Given also that \(M = 196\) when \(t = 50\), find the value of \(k\).
3. Obtain an expression for \(M\) in terms of \(t\) and find the least possible number of micro-organisms.