- The number of bacteria, \(N\), present in a liquid culture at time \(t\) hours after the start of a scientific study is modelled by the equation
$$N = 5000 ( 1.04 ) ^ { t } , \quad t \geqslant 0$$
where \(N\) is a continuous function of \(t\).
- Find the number of bacteria present at the start of the scientific study.
- Find the percentage increase in the number of bacteria present from \(t = 0\) to \(t = 2\)
Given that \(N = 15000\) when \(t = T\),
- find the value of \(\frac { \mathrm { d } N } { \mathrm {~d} t }\) when \(t = T\), giving your answer to 3 significant figures.