1. Define appropriate variables and parameters, and identify any constraints for the data. Independent variable: months
Dependent variable: temperature
Range: 13.5≤y≤26.9

2. Use technology to plot the data points on a graph. Comment on any apparent trends shown in the graph. By plotting the data given from the table into graphmatica, the graph below can be obtained. GRAPH 1

Temperature (℃)
Months

This graph shows that if we connect these points, we will see a regular wavy curve appropriately.

3. What type of function models the behavior of the graph? Explain why you chose this function. I noticed that the sine graph best models the behavior of the graph. The reason is that GRAPH 1 simply looks like a sine function and it seems contain amplitude and period.

Sine function graph : y=sin(x)

4. Use your knowledge of the graphs of such functions to create a suitable equation that models the behavior of the data. Explain all steps you took to arrive at your equation. First of all, the general sine function is defined as: y=AsinB(x-C)+D * A represent the Amplitude

* B represent the n in Period (T=2πn)
* C represent the Horizontal translation
* D represent the Vertical translation
* To find A, I know the ymin=13.5 and ymax=26.9 from the table. Amplitude = ymax-ymin2 = 26.9-13.52 = 6.7
A is therefore 6.7.
* To find B, I know that the period (T)=12 months.
T=2π BT=12
B = 2π12 = π6
B is therefore π 6.
* To find D, I know the ymin=13.5 and ymax=26.9 from the table. D= ymax+ymin2 =...

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