Step 3: Create a Mathematical Model Step 4: Use your Parametric Model to find the predicted x Work through the following steps to create two parametric equations where x is a function of t and y at each time point. and y is a function of t. Remember t is just a parametric variable. You are creating two 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*** Using your equations you found in step 3 to find the predicted x and y coordinates. Plug in the values t = 0, 1, 2, 3, and 4 into your parametric equations and enter your values for x and y in a. Plot x (longitude is the vertical axis) versus t (horizontal axis) (1 point) 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) What type of function or regression model do you think would best fit the data based x (longitude) y (latitude) predicted on your graphs? (1 points) predicted from model from model 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 !) 12 Use your calculator to create a formula for the model you have chosen. Enter the ordered pairs 3 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 = abt using the ExpReg. 4 feature on the calculator. If you think the function is quadratic your model will have the form y = at2 + bt + c using the QuadReg 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! Remember do not use a linear function! a. Plot your predicted x (table 2) and your actual x (table 1) versus time on one graph. The vertical axis is the longitude, and the horizontal axis is t. (1 pt) Directions to create this model on the TI84Plus Calculator at end of portfolio. b. Plot predicted y (table 2) and your actual y (table 1) versus time on one graph. The vertical d. Write your final equations: (2 points) axis is latitude and the horizontal axis is t. (1 pt). Make sure to submit the 2 graphs and label your axes and chose appropriate scales and ranges. Have a key indicating which data . x(t) are predicted and which are actual. For example use one color for predicted and one color for actual. . y(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