Storm Tracker Portfolio Worksheet
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.
Historical Hurricane XXXXXX
Take a screen XXXX of XXX XXXXXXXXX XXXX and include it XXXXX:
through XXX days along the XXXX. Note XXXX you XXXXX need XX use the XXXXXX XXXXX XXXXXXX XX XXX date XXXXXXXXXXX. In XXX table XXXXX, XXXXXX XXX record one point XXXX each XXX of XXX storm. XXXX each point t = 1, t = X, etc.
XXXXX the XXXXX for a total XX at least XXXX XXXX so XXXX you have a minimum of XXXX points in XXX table. Use the XXXXXXX XXXXX to XXXX you XXXX XXX XXXX, latitude, XXX longitude.
XXXX
t
x
(XXXXXXXXX)
y
(latitude)
Aug 15, XXXX
X
-XX.XX
24.25
XXX 16, 2017
XX.02
XXX 17, XXXX
-XX.04
XX.80
Aug XX, 2017
3
-101.XX
XX.XX
Aug XX, XXXX
-98.61
35.42
Step 3: XXXXXX a Mathematical XXXXX.
XXXX through the following XXXXX XX XXXXXX XXX XXXXXXXXXX equations where x is a function XX t and y XX a XXXXXXXX XX t.
XXXX a model of XXX form y = abx XXXXX the ExpReg XXXXXXX on the calculator.
· x(t) =0.XX^3 - X.XX^X - X.XX - XX.
XXXX in the XXXXXX t = X, 1, 2, X, and 4 into your parametric equations and XXXXXX XXXX values XXX x XXX y in the table XXXXX.
(longitude)
(XXXXXXXX)
-XX.X
XX.0
26.X
2
-XX.4
XX.6
-XXX.X
XX.4
-96.4
XX.X
XXX graph XXX x- and y-XXXXXXXXXXX from Table 1 onto graph XXXXX using XXX XXXXX, and XXXXX XXX x- and y-coordinates from Table 2 onto XXX same XXXXX paper XXXXX a different color. You may either copy and XXXXX your graph XXXX or upload it XXXXX with XXXX XXXXXXXXX.
Compare XXX model XXXXXX XXXX the original points XXX answer XXX XXXXXXXXX XXXXXXXXX:
XXX XXXX from XXXXX X XX smoother XXXX XXXX XX XXXXX 1. Besides XXXX, they XXX identitcal.
I chose the XXXXX graph XXXXXX XXXXXXX it XX a common graph XXXX is easier to observe
and XXXX XXX XXXXXXXXXXXXXXX. XXX choice is XXXX as the graph XX reproducible and XXXXXX
XXXXXXXXX, t, XXX write it as a rectangular equation XXXX x XXX y instead? XXX or why not?
No, it is XXX XXXXXXXX. Because x(t) XXXXXXXX XXX a XXXXXXXXXXX XX 3 (XXXX root in y(t)).
XXXXX, XXXXX is no mathematical XXXXXXXXXXXX that can be done to XXXXXX the
Step 3: Create a Mathematical Model.
XXXX XXXXXXX the following XXXXX to XXXXXX two parametric XXXXXXXXX where x XX a XXXXXXXX of t and y is a function of t.
XXXX a model of XXX form y = abx using the ExpReg XXXXXXX XX XXX XXXXXXXXXX.
· x(t) =X.4x^X - 1.XX^2 - X.XX - 92.
XXXX in the values t = X, 1, 2, 3, XXX X into your parametric XXXXXXXXX XXX insert XXXX values for x XXX y in XXX table below.
Now XXXXX the x- XXX y-coordinates from Table X XXXX XXXXX XXXXX XXXXX one color, and graph XXX x- and y-coordinates from XXXXX 2 XXXX XXX XXXX XXXXX XXXXX using a different color. You may either copy XXX paste your XXXXX here or upload it XXXXX with this XXXXXXXXX.
XXXXXXX XXX model points XXXX XXX original XXXXXX XXX answer XXX XXXXXXXXX questions:
The XXXX from Table X XX smoother XXXX that XX Table X. XXXXXXX XXXX, they are identitcal.
I chose the cubic graph family because it XX a XXXXXX graph that XX XXXXXX to XXXXXXX
and plot its XXXXXXXXXXXXXXX. XXX choice is well as XXX graph XX reproducible and easily
parameter, t, XXX write it as a XXXXXXXXXXX equation XXXX x and y instead? Why or why not?
No, it is not possible. Because x(t) XXXXXXXX has a XXXXXXXXXXX of 3 (XXXX root in y(t)).
XXXXX, XXXXX XX no mathematical XXXXXXXXXXXX that can be XXXX XX XXXXXX the