The bacterium, cholera, reproduces at an exponential rate which can be modeled through the continuous growth model. if the value for k is 1.38 and we initially start with 2 bacteria, what is the equation for cholera growth, where t is the number of hours?

The continuous growth rate model stipulates that the rate of population change  is in proportion with the actual population (a function of time ). That is, there is some such that



Solving for , you get



You're given that , so the population is increasing. At time , you start with 2 bacteria, so and



So, the growth equation is