Derivatives of Exponential, Logarithmic and Trigonometric Functions

The number of bacteria, \(n\), in a dish, after \(t\) minutes is given by \(n = 800\mathrm{e}^{0.13t}\).

1. Find the value of \(n\) when \(t = 0\).[2]
2. Find the rate at which \(n\) is increasing when \(t = 15\).[2]
3. After \(k\) minutes, the rate of increase in \(n\) is greater than \(10 \ 000\) bacteria per minute. Find the least value of \(k\), where \(k \in \mathbb{Z}\).[4]