The data below was generated from the Carbon Dioxide Starter File. The dark dots show the amount of CO2 in the atmosphere (in parts per million) recorded between December 2022 to November 2023. NOTE: the date column is the decimal year (so "June 15th, 2023" would be 2023.5).

date co2 (ppm)

2022.708

415.91

2022.792

415.74

2022.875

417.47

2022.958

418.99

2023.042

419.48

2023.125

420.30

2023.208

420.98

2023.292

423.36

2023.375

424.00

2023.458

423.68

2023.542

421.83

2023.625

419.68

2023.708

418.51

Scatter plot showing global CO2 levels over time, rising from December 2022 to May 2023, then dropping to December 2023. a few lighter dots are present from before December 2022 to hint at the nature of the curve.

1 Connect the dark dots on the scatter plot from left to right to form a line-graph of the data in recent-table.

2 The amount of CO2 varies from the lowest valley to the highest peak.

3 This represents a change in atmospheric CO2 of difference between highest and lowest parts per million.

4 Find the amplitude (a) by cutting the vertical distance you calculated in half: CO2 in the atmosphere in parts per million

5 Draw the midline on the graph. (It should be a horizontal line passing in the middle between the lowest valley and the highest peak.)

6 The midline makes the vertical shift (k) visible. What is the vertical shift (k) of the model? CO2 in the atmosphere in parts per million

HINT: The vertical shift can also be calculated by adding the amplitude(a) to the valley.

7 The phase shift (h) is the decimal year when the data first crosses the midline. Estimate The phase shift (h) years

8 Calculate the period between the valleys: 2023.708date for the lowest values in 2023 - 2022.792date for the lowest values in 2022 = years (round to the nearest full year)

9 If   $$\displaystyle \textbf{period} = {2\pi \over\displaystyle \text{frequency}}$$   then   $$\displaystyle \textbf{frequency} = {2\pi \over\displaystyle \text{period}}$$.   How do you know that this statement is true?

10 What is the frequency (b) of this model?

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