9.4 Differential Equations
Population Growth Model
Question #3 (Medium): Solving the Logistic Equation for Popualtion Increase
Logistic model expresses population to be ( ) where is the carrying capacity and is the
relative growth rate constant factor and where is the initial population.
Biologist have discovered that dolphin population at a certain part of the Pacific ocean is . They have
also estimated the carrying capacity to be . In that part of the ocean, the dolphin population has
doubled over the past year.
1) Assuming that the dolphin population satisfies the logistic equation, find the expression for the
population size after ye