Here is another way to derive the logistic model you first saw on page 31. Consider an area of grassland that has enough resources to support a buffalo population of size k (k is called the grassland's carrying capacity for buffalo). The key assumption that this model makes is the following: the per capita rate of change of the population is proportional to the fraction of resources available

The fact that the carrying capacity is k means that when there are exactly k individuals in the population, they are utilizing 100 % of the resources. In that case, what fraction of the resources are used by one individual?