3. The number of bacteria in a liquid culture is modelled by the formula
$$N = 3500 ( 1.035 ) ^ { t } , \quad t \geqslant 0$$
where \(N\) is the number of bacteria \(t\) hours after the start of a scientific study.
- State the number of bacteria at the start of the scientific study.
(1) - Find the time taken from the start of the study for the number of bacteria to reach 10000
Give your answer in hours and minutes, to the nearest minute. - Use calculus to find the rate of increase in the number of bacteria when \(t = 8\) Give your answer, in bacteria per hour, to the nearest whole number.