A catfish farm: Catfish in a commercial pond can be expected to exhibit logistic population growth. Consider a pond with a carrying capacity of K = 4000 catfish. Take the r value for catfish in this...

A catfish farm: Catfish in a commercial pond can be expected to exhibit logistic population growth. Consider a pond with a carrying capacity of K = 4000 catfish. Take the r value for catfish in this pond to be r = 0.06.

a. Write the equation of change for logistic growth of the catfish population. (Hint: If you have difficulty here, refer to Example 6.10.)

 b. Make a graph of dN dt versus N.

c. For what values of N would the catfish population be expected to increase?

 d. For what values of N would the catfish population be expected to decrease?

 e. Recall from Section 5.1 that the maximum sustainable yield model says that a renewable resource should be maintained at a level where its growth rate is at a maximum, since this allows the population to replenish itself quickly. According to this model, at what level should the catfish population be maintained?