The population, \(P\), of a certain bacterium \(t\) days after the start of an experiment is modelled by

\(P=800e^{kt},\)

where \(k\) is a constant.

(i) State what the figure \(800\) represents in this experiment.

(ii) Given that the population is \(20000\) two days after the start of the experiment, calculate the value of \(k\).

(iii) Calculate the population three days after the start of the experiment.