Name Date Storm Tracker Portfolio Worksheet (Alternate) 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, meteorologists can apply that knowledge to future weather events. Parametric equations can be used to graph the path of an object in space. For example, they can be used to describe the path of a storm moving through an area. In this portfolio, you will use historical storm data to trace the path of a hurricane. From this data, you will use parametric equations to model the path of the storm. Step 1: Analyze Hurricane Beryl of 1994 The table below shows the latitude and longitude of Hurricane Beryl at different times on each day from August 14 to August 19, 1994. Step 1: Analyze Hurricane Beryl of 1994 The table below shows the latitude and longitude of Hurricane Beryl at different times on each day from August 14 to August 19, 1994. Date Latitude Longitude August 14 28.69 87.30 August 14 29.44 -87.39 August 15 29.52 -86.29 August 15 29.65 -85.89 August 15 29.65 -85.65 August 15 29.88 85.72 August 16 30.05 -85.65 August 16 30.18 -85.52 August 16 30.37 -85.39 August 16 31.30 -85.08 August 16 32.38 -84.55 August 17 33.28 83.98 August 17 34.33 -83.63 August 17 35.42 -82.62 August 17 37.53 -81.54 August 18 38.46 -79.63 August 18 39.55 -77.54 August 18 41.20 -76.07 August 18 41.69 -73.89 August 19 42.03 -71.98 NOAA Historical Hurricane Track DataStep 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 August 14 and make this date t = 0. 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 five days so that you have five points in the table. Table 1 X y (longitude) (latitude) Date t ALUMI-'D 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. 1. First plot t versus x, then plot t versus y. What kind of regression should you use for each one based on your graphs? 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 line of best fit for your model. For example, if your path appears to be exponential, you will have a model of the form yzabx using the Epreg feature on the calculator. 3. Write your final equations: I x(t) = - W) = SEEP 2!: CHECK VOUI\" lVloElel 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 t X y (longitude) (latitude) 0 1 2 3 4 Now graph the x- and ycoordinates from Table 1 onto graph paper using one color, and graph the x- and ycoordinates from Table 2 onto the same graph paper using a different color. 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 answer the following quesons: 1. How does your model compare to the actual path? 2. Why did you choose the graph family that you did? Did you choose well? Why or why not? 3. Is it possible to solve x(t) for t, substitute it into y(t) to eliminate the parameter, t, and write it as a rectangular equation with x and y instead? Why or whv not