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 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. 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 y=ab* using the ExpReg feature on the calculator.
3. Write your final equations:
X(t)=?
Y(t)=?
Step 4: Check Your Model
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.
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. 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 questions:
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 xt) 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 why not
