A scientist conducts an experiment on the growth of a certain bacteria. The variable t represents the number of hours since the beginning of the experiment. When t = 0 (that is, at the beginning of the experiment), there were 150 bacteria in the culture. Every 1 hour, the number of bacteria in the culture increases by a factor of 3.

The number of bacteria in the culture, N, can be modeled as a function of t by an exponential growth function N(t). An exponential growth function N(t) is a function of the form ()=(), where c and k are positive constants.