Chapter 3.4, Problem 171E

For the following exercises, consider an astronaut on a large planet in another galaxy. To learn more about the composition of this planet, the astronaut drops an electronic sensor into a deep trench. The sensor transmits its vertical position every second in relation to the astronaut’s position. The summary of the falling sensor data is displayed in the following table.

Time after dropping (s)	Position (m)
0	0
1	-1
2	-2
3	-5
4	-7
5	-14

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.

171. [T] The Holling type I equation is described by

   $f\left(x\right)=ax$, where x is the amount of prey available and a >0 is the rate at which the predator meets the prey for consumption.

1. Graph the Holling type I equation, given a = 0.5.
2. Determine the first derivative of the Holling type I equation and explain physically what the derivative implies.

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

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