# Is the data set approximately periodic? If so, what are its period and amplitude? | Hour | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Number of cars | 52 | 76 | 90 | 75 | 91 | 104 | 89 | 105 | 119 | 103 | 121 | 135 | not periodic - periodic with period of 3 and amplitude of about 7.5 - periodic with period of 3 and amplitude of about 15 - periodic with period of 4 and amplitude of about 7.5
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Answer

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Step 1:
I'll solve this step-by-step to determine if the data set is periodic and identify its potential period and amplitude.

Step 2:
: Understand Periodicity

Periodicity means a pattern that repeats at regular intervals. To check this, I'll look for consistent cyclic behavior in the data.

Step 3:
: Calculate Differences Between Consecutive Data Points

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Let's examine the differences between consecutive values: \text{Hour Interval} & \text{Difference} \ \hline 1 \to 2 & 76 - 52 = 24 \ 2 \to 3 & 90 - 76 = 14 \ 3 \to 4 & 75 - 90 = - 15 \ 4 \to 5 & 91 - 75 = 16 \ 5 \to 6 & 104 - 91 = 13 \ 6 \to 7 & 89 - 104 = - 15 \ 7 \to 8 & 105 - 89 = 16 \ 8 \to 9 & 119 - 105 = 14 \ 9 \to 10 & 103 - 119 = - 16 \ 10 \to 11 & 121 - 103 = 18 \ 11 \to 12 & 135 - 121 = 14 \end{array}

Final Answer

While there's a rising and falling pattern, it doesn't show a consistent, repeating cycle with a fixed period and amplitude. The correct option is: "not periodic" Key Observations: - No consistent 3 -step or 4 -step repeating pattern - Overall trend seems to be generally increasing - Significant variation between data points - Lacks the mathematical definition of true periodicity