The hourly rate of increase of a bacteria colony is equal to 5% of the current size of the colony. N N\,N is the number of bacteria in thousands and t t\,t is the time in hours.
Write down a differential equation for this relationship.
Show that N=Ae0.05tN = Ae^{0.05t}N=Ae0.05t where A A\,A is a constant.
Given that the initial number of bacteria is 4000. Find the number of bacteria after 8 hours to 3 significant figures.
