Question # 7
Answer:
Yes. It displays exponential behavior.
To determine:
We have to determine whether the set of data shown above displays exponential behavior. Write Yes or No. Explain why or why not
Solution Steps:
Considering the set of data
x 2 5 8 11
y 480 120 30 7.5
To determine whether the set of data shown above displays exponential behavior, we would first need to check the pattern of x and y values.
The set of data will be exponential if
- there is a constant change in x
- there is a constant ratio in y
From the data set, it is clear that there is a constant change in the values of x. For example,
- 2 + 3 = 5
- 5 + 3 = 8
- 8 + 3 = 11
Also, there is a constant ratio in y. For example,
- 480 / 120 = 4
- 120 / 30 = 4
- 30 / 7.5 = 4
So, from this observation we can conclude that the the set of data shown above displays exponential behavior.
Therefore, my answer is Yes. It displays exponential behavior.
The graph in figure a is also attached below for visual aid.
Question # 8
Answer:
No. It does not display exponential behavior.
To determine:
We have to determine whether the set of data shown above displays exponential behavior. Write Yes or No. Explain why or why not
Solution Steps:
Considering the set of data
x 21 18 15 12
y 30 23 16 9
To determine whether the set of data shown above displays exponential behavior, we would first need to check the pattern of x and y values.
The set of data will be exponential if
- there is a constant change in x
- there is a constant ratio in y
From the data set, it is clear that there is a constant change in the values of x. For example,
- 21 - 3 = 18
- 18 - 3 = 15
- 15 - 3 = 12
BUT! there is NOT a constant ratio in y. For example,
- 30 / 23 = 1.30
- 23 / 16 = 1.44
- 16 / 9 = 1.78
INSTEAD, there is a constant change in y values. i.e. 30 - 7 = 23, 23 - 7 = 16, 16 - 7 = 9 ; meaning it represents LINEAR BEHAVIOR.
So, from this observation we can conclude that the the set of data shown above DOES NOT display exponential behavior. Instead, it displays LINEAR Behavior because there is constant change in x and y values.
Therefore, my answer is No. It does not display exponential behavior.
The graph in figure b is also attached below for visual aid.
Keywords: exponential behavior, exponential function, linear function
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