A biologist is studying the growth rate of a certain species of bacteria in a controlled environment. The growth of the bacteria can be modeled by the equation:

$$P(t) = P_0 e^{rt}$$

where:

• $$P(t)$$ is the population at time $$t$$,
• $$P_0$$ is the initial population,
• $$r$$ is the growth rate (expressed as a decimal),
• $$t$$ is the time in hours.

Initially, there are 500 bacteria, and they double in size every 3 hours. What is the growth rate $$r$$ expressed in terms of natural logarithms (i.e., base $$e$$)?