In a certain chemical reaction, the amount, \(x\) grams, of a substance is increasing. The differential equation satisfied by \(x\) and \(t\), the time in seconds since the reaction began, is

\[ \frac{dx}{dt} = kx e^{-0.1t}, \]

where \(k\) is a positive constant. It is given that \(x = 20\) at the start of the reaction.

(a) Solve the differential equation, obtaining a relation between \(x\), \(t\), and \(k\).

(b) Given that \(x = 40\) when \(t = 10\), find the value of \(k\) and find the value approached by \(x\) as \(t\) becomes large.