During a research experimentit was found that the number of bacteria in a culture grew at a rate proportional to its size. At 9am there were 2000 bacteria present. At noon the number of bacteria grew to 2,700. How many bacteria will there be at midnight?

A model that describes the expotential uninhabitedgrowth of a population P, after a certain time t, is

P(t)= P o e^kt

Where P o = P (0)is the initial populationand k>0 is a constant called the relative growth rate.