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. 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***
Plot x (longitude is the vertical axis) versus t (horizontal axis) (1 point)
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 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 on your graphs? (1 points)
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 t) ___________________
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 = abt using the ExpReg 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!
Directions to create this model on the TI84Plus or Desmos Calculator are at end of portfolio.
d. Write your final equations: (2 points)
x(t) =
y(t) =
e. Based on the graphs and data, the best fit function for x (longitude versus t) appears to be a quadratic function.
f. The best fit function for y (latitude versus t) seems to be a linear function.
g. Final Equations:
x(t) = at^2 + bt + c
y(t) = mt + n