Chapter 3.4, Problem 172E

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

172.

[T] The Holling type II equation is described by

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

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

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

Holling type I and II equations?

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

c. Show that $f\left(n\right)=\frac{1}{2}a$ and interpret the meaning of

the parameter n.

d. Find and interpret the meaning of the second derivative. What makes the Holling type II function more realistic than the Holling type I function?