The number of bacteria, \(N\), in a culture after \(t\) hours is modelled by the formula \(N=500\left(2^{1.0566t}\right)\).
Calculate the number of bacteria after 200 minutes.[1]
An antibiotic is effective only if it is administered before the number of bacteria reaches 25 000. If the bacteria is introduced to the culture at 9.30 am, explain if the antibiotic is effective if it is administered at 2.45 pm.[4]
Explain whether this formula is still valid in the long run.[1]