Modeling the Weather
The table shows Melbourne’s mean average daily maximum temperature (℃) for two year period 1999-2000.
Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
1999 | 25.7 | 26.9 | 24.5 | 21.4 | 18.0 | 14.0 | 13.5 | 13.9 | 17.2 | 19.4 | 22.2 | 24.6 |
2000 | 26.0 | 25.4 | 24.7 | 20.7 | 17.5 | 14.6 | 14.8 | 14.4 | 17.5 | 20.6 | 22.9 | 26.1 |
1. Define appropriate variables and parameters, and identify any constraints for the data.
Independent variable: months
Dependent variable: temperature
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.
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.
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... [continues]
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