3 The profit \(\pounds P\) made by a company in its \(n\)th year is modelled by the exponential function $$P = A \mathrm { e } ^ { b n }$$ In the first year (when \(n = 1\) ), the profit was \(\pounds 10000\). In the second year, the profit was \(\pounds 16000\).

1. Show that \(\mathrm { e } ^ { b } = 1.6\), and find \(b\) and \(A\).
2. What does this model predict the profit to be in the 20th year?