A scatter plot can help you to visualize the behavior of the data and decide the appropriate model.
See solution.
Practice makes perfect
Let's consider a real-life situation, then we can decide which model is appropriate for it. In an attempt to save the American Plains bison from extinction, the US government, along with private landowners, established protected herds in the early 1900's. They had plentiful resources and few predators, so they grew quickly.
Number of Bison
21
25
32
36
37
48
63
70
91
108
131
149
182
225
Years after 1900
2
3
4
5
6
7
8
9
10
11
12
13
14
15
The table above shows the number of bison each year, starting from 1902.
We can draw a scatter plot of this data to visualize its behavior and identify which model is appropriate for this situation.
As we can see, the data suggests using an exponential model. We can perform an exponential regression by entering the data in a graphing calculator. Then we press STAT, scroll to view the CALC options, and then choose ExpReg. We should obtain the results shown below.
We can round the parameters to the third decimal place and use a ≈ 14.244 and b ≈ 1.2.
The graph above shows how well the exponential function used describes the data points. Notice that there infinitely many real-life situations that can be modeled using the functions mentioned in Exploration 1. This is just one example.
