# The following problems deal with the Holling type I, II, and III equations.

These equations describe the ecological event of growth of a predator population given the amount of prey available for consumption.

The Holling type I equation is described by f(x)=ax, where x is the amount of prey available and a>0 is the rate at which the predator meets the prey for consumption.

a. Graph the Holling type I equation, given a=0.5.

b. Determine the first derivative of the Holling type I equation and explain physically what the derivative implies.

c. Determine the second derivative of the Holling type I equation and explain physically what the derivative implies.

d. Using the interpretations from b. and c. explain why the Holling type I equation may not be realistic.

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