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Date: Name: Storm Tracker Portfolio Worksheet PRECALCULUS: PARAMETRIC FUNCTIONS Directions: Meteorologists use sophisticated models to predict the occurrence, duration, and trajectory of weather events. They build their models based on observations that they have made in the past. By understanding how previous weather events evolved, meteooogists can apply that knowledge to future weather Parametric equations can be used to graph the path of an object in space. For example, used to describe the path of a storm moving through an area. they can be In this portfolio, you will use historical storm data to trace the path of a hurricane. From th is data, you will use parametric equations to model the path of the storm. Step 1: Analyze Hurricane George of 1980 The table below shows the latitude and longitude of Hurricane George at different times on each day from September 1 to September 8 1980. Longitude Date Latitude 38.0 15.6 16.3 16.8 17.3 September 1 September 1 September 1 September 2 September 2 September 2 September 2 September 3 September 3 September 3 September 4 September 4 September 4 September 5 September 5 September 5 September 5 September 6 September 6 40.8 -42.1 -43.7 -45.7 17.5 -48.1 17.7 17.8 50.3 54.5 56.9 18.0 18.6 19.7 21 22.1 23.4 26.1 -59.0 -61.0 -62.3 -63.6 -65.8 -68.6 28.5 69.4 -70.0 -69.6 -69.1 29 30.6 31.7 32.9 Step 2: Plot the Hurricane Path Use the data from step 1 to make a table of the storm's horizontal and vertical movement with respect to time. Start with a data point provided in the table in step 1 from September 1 and make this date t-O. Note the position's latitude and longitude and record them in Table 1. Since latitude measures north/south and longitude measures east/west, the latitude coordinate will be y and the longitude coordinate will be x. Now progress through the days along the path. Choose and record one point from each day of the storm. Mark each point t- 1,t-2, etc. Track the storm for a total of 6 days so that you have 6 points in the table. Table 1 | Date t.1X(longitude) | y (latitude) 0 4 Step 3: Create a Mathematical Model Work through the following steps to create two parametric equations where x is a function of t and y is a function of t.* *If you use a linear regression for this portfolio the highest grade you are able to earn is a 70*** 1. First plot t versus x, then plot t versus y. What type of function or regression model do you think would best fit the data based on your graphs? Make sure to add the graph for your instructor to view 2. Use your calculator to create a formula for the model you have chosen. Enter the ordered pairs into lists and have the calculator create the best fit function for your model. For example, if your path appears to be exponential, you will have a model of the form y- ab using the ExpReg feature on the calculator. 3. Write your final equations: x(t) y(t)- Step 4: Check Your Model Using your equations you found in step 3, plug each t-value in and solve. Plug in the values t 0, 1, 2, 3, and 4 into your parametric equations and insert your values for x and y in the table below. Table 2 y (latitude) x (longitude 0 2 3 4 5 Now graph the x- and y-coordinates from Table 1 onto graph paper using one color, and graph the x- and y-coordinates from Table 2 onto the same graph paper using a different color. Be sure to label which color is which dataset. You may either copy and paste your graph here or upload it along with this worksheet. Compare the model points with the original points and questions: answer the following 1. How does your model compare to the actual path? 2. Why why not? id you choose the graph family that you did? Did you choose well? Why or . In 3. Is it possible to write this in rectangular form, eliminating the parameter t other words express y in terms of x (eliminate the parameter t and h function, y -f(x)) Why or why not? ave one Turn it in: . Upload this worksheet into the Drop Box. . If you did not paste a copy of your graph into the worksheet, be sure to also upload the graph into the Drop Box.

Answer 1

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