Year 10 Maths Hl Modeling the Weather
Year 10 Mathematics HL Portfolio
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
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 =
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
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 =