The growth rate of a population that has a limited food supply will most likely be

The growth rate of a population that has a limited food supply will most likely be LOGISTIC. 

For as long as there is enough resources for a population, the growth rate of the population would increase. Growth however cannot go on forever because no matter what, resources will start to deplete. The growth rate of the population will then start to decrease as the number of individuals increase and when this happens, it means that a logistic population growth has occurred.