A population, \(B\), of a particular bacterium, \(t\) hours after measurements began, is given by

\(B=1000e^{t/4}.\)

(i) Find the value of \(B\) when \(t=0\).

(ii) Find the time taken for \(B\) to double in size.

(iii) Find the value of \(B\) when \(t=8\).