Question

Decide whether the data in the table represent a linear function or an exponential function. Explain how you know.
x y
1 162
2 54
3 18
4 6
5 2
A. The data represent an exponential function because there is a common ratio of 3.
B. The data represent a linear function because there is a common difference of 108.
C. The data represent a linear function because there is a common difference of –108.
D. The data represent an exponential function because there is a common ratio of 1/3.

Answer 1

It is an exponential function because it has a common ratio of 1:3

Answer 2

Solution:

1. We will plot the points on the coordinate plane, if they lie in a line it means they are linear.

2. Find the slope between each two points ,if you don't want to plot these points on coordinate plane,then by using the formula of slope between two points which is , =$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ ,if slopes are same between any two points it means these points are collinear.

As you can see in the coordinate plane that these points are not collinear.

Now , $\frac{y}{x}=\frac{\text{First term}}{\text{Second term}}=\frac{162}{54}=\frac{54}{18}=\frac{18}{6}=\frac{6}{2}=3$

It means this is a geometric progression because $\frac{\text{Second term}}{\text{First Term}}=\frac{1}{3}$

Option D : The data represent an exponential function because there is a common ratio of 1/3. is true statement.