Lesson 3: Functions

Math 10C Module 4: Lesson 3

Module 4: General Relations

Going Beyond

This shows a photo of an accelerating cheetah.

This shows a photo of a walking gazelle.

Functions can be used to predict future events. The following is an example.

The cheetah is a member of the cat family known for its speed. In fact, the cheetah can accelerate from rest to 96 km/h in 3 s! Cheetahs are carnivores, known to stalk hoofed animals such as the Thomson’s gazelle. The gazelle, also a swift animal, can run as fast as 80 km/h.

A cheetah is stalking a gazelle in the Serengeti Grasslands. The cheetah has approached the gazelle to within a distance of 70 m.

Suddenly, the gazelle senses trouble and starts to bolt. The cheetah instantly gives chase! After 5 seconds, assume that both the cheetah and gazelle are running at their maximum speed. You can use a graph (with labelled axes and a title) to figure out whether the cheetah will be able to catch the gazelle.

Cheetah		Gazelle
t (s)	d (m)	t (s)	d (m)
5.0	93.3	5.0	126.3
6.0	120.0	6.0	148.5
7.0	146.7	7.0	170.7
8.0	173.3	8.0	192.9
9.0	200.0	9.0	215.1
10.0	226.7	10.0	237.3

This shows a graph of the positions of a cheetah and a gazelle over a 15-second interval.

What do the data table and the graph tell you?
Will the cheetah’s hunt be successful this time? If so, how long will the hunt take?