Chapter 3.4, Problem 173E

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

173. [T] The Holling type III equation is described by

   $f\left(x\right)=\frac{a{x}^2}{n^2+x^2}$ , where x is the amount of prey available

and a >0 is the maximum consumption rate of the predator.

1. Graph the Holling type III equation given a = 0.5 and n = 5. What are the differences between the
Holling type II and III equations?

Take the first derivative of the Holling type III equation and interpret the physical meaning of the derivative.

Find and interpret the meaning of the second derivative (it may help to graph the second derivative).

What additional ecological phenomena does the Holling type III function describe compared with the Holling type II function?