.DIRECTIONS: Before beginning, select FILE > MAKE A COPY of this Google Doc. Complete the portfolio and then convert the final submission to PDF (Download as a pdf or print as a pdf) and submit in Portfolio Step 2: Plot the Hurricane Path Drop Box.* ***# Name: Date: 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 26 and Storm Tracker Portfolio Worksheet make this date t = 0. Note the position's longitude and latitude and record them in Table 1. PRECALCULUS: PARAMETRIC FUNCTIONS 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. Directions: Meteorologists use sophisticated models to predict the occurrence, duration, and Choose and record one point from each day of the storm. Mark each point t = 1, t = 2, etc. trajectory of weather events. They build their models based on observations that they have Track the storm for a total of 5 days so that you have 5 points in the table, one from each day of made in the past. By understanding how previous weather events evolved, meteorologists can the storm. apply that knowledge to future weather events. For example: Parametric equations can be used to graph the path of an object in space. For example, they can Pick one of the data points for September 26 be used to describe the path of a storm moving through an area. In this portfolio, you will use This point ist = 0 historical storm data to trace the path of a hurricane. From this data, you will use parametric Record the x (longitude) and y (latitude) coordinates in Table 1 equations to model the path of the storm. Pick one of the data points for September 27. This point is t=1 Step 1: Analyze Hurricane IAN of 2022 Record the x (longitude) and y (latitude) coordinates in Table 1 The table below shows the latitude and longitude of Hurricane IAN at different times on each day Repeat for September 27 28, 29 and 30 which will be t=2, 3, 4, 5 from September 26th to September 30"h 2022. Table 1 Actual data collected x and y Date Latitude Longitude Wind Sep 26 18.2 -82 75 mph Date t x (longitude) y (latitude) Sep 26 18.7 -82.4 75 mph (East/West) (North/South) 18.2 -82 Sep 26 19.1 -82.7 80 mph Sep 26 Sep 27 20.8 -83.3 100 mph 1 20.8 -83.3 Sep 27 Sep 27 21.3 83.4 105 mph Sep 38 2 24.4 83 Sep 27 21.7 83. 110 mph Sep 29 27.2 -81.7 Sep 28 24.4 -83 120 mph Sep 28 24.5 83 120 mph 4 29.7 -79.4 Sep 30 Sep 28 24.6 32.9 120 mph Sep 29 27.2 -81.7 115 mph Sep 29 27.3 81 6 105 mph Sep 29 27 4 81.5 100 mph Sep 30 29.7 79.4 15 mph Sep 30 30.2 79.3 60 mph Sep 30 30.2 79.3 85 mphStep 3: Create a Mathematical Model Work through the following steps to create two parametric equations where x is a function of t Step 4: Use your Parametric Model to find the predicted x and y is a function of t. Remember t is just a parametric variable. You are creating two and y at each time point. functions x(t) and y(t) ***If you use a linear regression for this portfolio the highest grade you are able.to earn is a 70*2* Using your equations you found in step 3 to find the predicted x and y coordinates. Plug in the a. Plot x (longitude is the vertical axis) versus t (horizontal axis) (1 point) values t - 0, 1, 2, 3, and 4 into your parametric equations and enter your values for x and y in the table below. b. Plot y (latitude is the vertical axis) versus t horizontal axis. These should be two separate graphs. Make sure to submit the 2 graphs for your instructor to view. Label Table 2 Predicted x & y from your model's equation (2 points) your axes and chose appropriate scales and ranges for your axis. Include a title for each graph. (1 point) rt x (longitude) y (latitude) predicted c. What type of function or regression model do you think would best fit the data based predicted from model from model on your graphs? (1 points) 0 What type of function will you be using for x (longitude versus t) What type of function will you be using for y (latitude versus !) 3 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 4 path appears to be exponential, you will have a model of the form y = ab using the ExpReg feature on the calculator. If you think the function is quadratic your model will have the form y = at? + bt + c using the QuadReq feature on the calculator. You will then do the same for x. You do not have to use the same model type for both x and y. Pick the model that fits each one best! a. Plot your predicted x (table 2) and your actual x (table 1) versus time on one graph. The Remember do not use a linear function! vertical axis is the longitude, and the horizontal axis is t. (1 pt) Directions to create this model on the T184Plus Calculator at end of portfolio. b. Plot predicted y (table 2) and your actual y (table 1) versus time on one graph. The vertical axis is latitude and the horizontal axis is t. (1 pt). Make sure to submit the 2 graphs and d. Write your final equations: (2 points) label your axes and chose appropriate scales and ranges. Have a key indicating which data are predicted and which are actual. For example use one color for predicted and one color for x(t) = actual. v (t) = C. Visually compare the actual and predicted data on the plots? Do they seem to be similar? If not consider using a different model and repeating part 3d and Step 4.Now graph the actual x- and y-coordinates from Table 1 using one color and graph the predicted Directions for finding a function using data points on the TI 84 Plus or modeled x- and y-coordinates from Table 2 onto the same graph using a different color. Your x coordinates are the horizontal axis and your y coordinates are the vertical axis. Be sure to To enter values to find the function Hit STAT label which color is which dataset. You may either copy and paste your graph here or upload it Hit 1: Edit 71 84 Pivl along with this worksheet. To clear all values in table use arrows to go to column heading, hit CLEAR and then ENTER 1. How does your model compare to the actual path? Be specific and write at least 2 sentences supporting your conclusion (1 pt) Enter values in lists as needed. Hit ENTER after each entry Use arrows to move between and within lists To find the regression model Hit STAT Arrow over to CALC 2. Why did you choose the graph family that you did? Did you choose well? Why or why not? (1 Choose the function you want - there are two screens of pt) choices. Consider: 5 QuadReg,- Quadratic at? +bt + c 6 CubicReg - Cubic at3 +bt? + ct. + d 7 QuartReg - Quartic at* +bt3 + ct2 + dt + e 0 ExpReg - Exponential abt A PurReg - Power atb 3. Is it possible to write this in rectangular form, eliminating the parameter t. In other words express y in terms of x (eliminate the parameter t and have one function, y =f(x)) Why or why TI-84 Plus C Silver Edition TI-84 Plus C Silver Edition not? (1 pt) TEXAS INSTRUMENTS TEXAS INSTRUMENTS NORMAL FLOAT AUTO REAL DEGREE HP NORMAL FLOAT AUTO REAL DEGREE MP EDIT CALC TESTS 1:1-Var Stats EDIT CALC TESTS 2:2-Var Stats 71QuartReg 3:Med-Med 8: LinReg(a+bx) 4:LinReg(ax+b) 9: LnReg O: ExpReg Turn it in: S: QuadReg A: PurRes 6: CubicRes 7:QuartReg B: Logistic . Upload this completed worksheet into the Drop Box. You should have 5 clearly labeled 8:LinRes(a+bx) C : SinReg D: Manual-Fit Y=mX+b graphs with titles and axes labeled. The required graphs are: 94LnRe9 EQuickPlot&Fit-EQ Actual x versus t Actual y versus t Overlaid graph of Modeled and Actual x versus t Overlaid graph of Modeled and Actual y versus t Overlaid graph of Modeled and Actual x and y coordinates. For all graphs, make sure to label your axis and use an appropriate scale and for overlaid graphs include a key indicating what is each graph. . If you did not paste a copies of your graphs into the worksheet, be sure to also upload the graphs into the Drop Box. Clearly label what is in each file