Final answer:
The given differential equation dp/dt = 3p can be solved by separating the variables and integrating, resulting in an exponential growth function P(t) = ae3t for a given initial condition P(0) = a.
Step-by-step explanation:
The question involves solving a differential equation of the form dp/dt = 3p, which describes exponential population growth.
To solve this equation, we can separate variables and integrate both sides.
This results in the general solution P(t) = Ce3t, where C is the integration constant that would generally be determined by an initial condition such as an initial population size at time t = 0.
For a non-zero constant a, the specific solution would be P(t) = ae3t if we were given P(0) = a.
The information provided also connects to the logistic growth model and exponential growth rates in the context of population dynamics.
While the logistic growth model and its application are not explicitly solved here, it's mentioned as a more complex scenario for modeling population growth when limiting factors are considered.