The population P(t) of a bacteria culture after t hours is modelled by the function P(t)=P02t/4, where P0 is the initial population.
a. (i) If the culture starts with P0=5×103 bacteria, form an equation to determine the time t when the population reaches 8×104 bacteria.
b. (ii) Solve the equation obtained in part (i) and find t correct to the nearest hour.