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Precalculus Portfolio
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Name Date </p> <p> </p> <p><strong>Storm Tracker Portfolio Worksheet</strong> </p> <p><strong>PRECALCULUS: PARAMETRIC FUNCTIONS</strong> </p> <p> </p> <p><strong>Directions: </strong>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. </p> <p>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. </p> <p> </p> <h1>Step 1: Find your hurricane.</h1> <ul><li>Select the link to access the NOAA’s Office for Coastal Management: Historical Hurricane Tracks website to search for a hurricane. </li><li>Type any state in the search box. (Note: Inland states do not usually have hurricanes. Type in a different state if no hurricanes are listed.) </li><li>Select one hurricane from the list that XXXXXXX. </li><li>XXXXXX <em>XXXX XX Storm </em>above XXX XXXX to XXXX the XXXX hurricane path. </li><li> </li><li>XXXX a table of the storm’s horizontal XXX vertical XXXXXXXX with respect to time. XXXXX XXXX a XXXXXXXX XXXXX on XXX path XXX XXXX the XXXXXXXXXXX date in XXX table XX XXX XXXX. XXXX this date <em>t </em>= 0. XXXX XXX XXXXXXXX coordinates from XXX lower XXXX corner XX the XXX view and record them in Table X. XXXXX XXXXXXXX XXXXXXXX north/XXXXX and longitude measures XXXX/west, the first coordinate will XX <em>y </em>XXX the second coordinate will XX <em>x</em>. XXX XXXXXXXX <br> </li><li>XXXXXX XXXX worksheet into XXX Drop Box. </li><li>XX you did XXX paste a XXXX XX your XXXXX into XXX worksheet, be sure to also XXXXXX the graph XXXX the Drop XXX. </li></ul> <p><u>XXXXXXXXXX XXXXXXXXX Tracks</u> </p> <p> </p> <h1>XXXX X: Plot the XXXXXXXXX XXXX.</XX> <p> <img XXX="file:///C:\XXXXX\XXXXX\XXXXXXX\Local\Temp\msohtmlclip1\XX\XXXXXXXXXXXXX.jpg" width="360" height="XXX"><XX></p> <table> <tbody><tr> <td> <br></td></tr> <tr> </tr> </tbody></table> <p> XXXX a screen shot XX XXX hurricane XXXX XXX XXXXXXX it below: <br></p> <p>through XXX XXXX XXXXX the path. XXXX that you might XXXX to XXX the XXXXXX arrow closest to XXX date XXXXXXXXXXX. In the table below, XXXXXX and XXXXXX XXX XXXXX XXXX each XXX of XXX storm. Mark XXXX XXXXX <em>t </em>= 1, <em>t </em>= X, etc. </p> <p>Track the XXXXX XXX a XXXXX of XX least five XXXX so that you XXXX a minimum XX five XXXXXX in XXX table. Use the XXXXXXX below XX help you XXXX the XXXX, latitude, and XXXXXXXXX. </p> <p> </p> <h2>XXXXX 1</XX> <p> </p> <table> <tbody><tr> <td> <p>XXXX </p></td><td> <p><em>t</em> </p></td><td> <p><em>x</em> </p><p>(XXXXXXXXX) </p></td><td> <p><em>y</em> </p><p>(latitude) </p></td></tr> <tr> <td> <p>XXX XX, 2017 </p></td><td> <p>X </p></td><td> <p>-XX.76 </p></td><td> <p>XX.25 </p></td></tr> <tr> <td> <p>XXX XX, 2017 </p></td><td> <p>X </p></td><td> <p>-XX.XX </p></td><td> <p>27.XX </p></td></tr> <tr> <td> <p>Aug XX, XXXX </p></td><td> <p>2 </p></td><td> <p>-XX.04 </p></td><td> <p>29.XX </p></td></tr> <tr> <td> <p>XXX 18, 2017 </p></td><td> <p>3 </p></td><td> <p>-101.XX </p></td><td> <p>XX.44 </p></td></tr> <tr> <td> <p>XXX 19, 2017 </p></td><td> <p>X </p></td><td> <p>-XX.XX </p></td><td> <p>XX.42 </p></td></tr> </tbody></table> <p> </p> <p><strong>XXXX 3: Create a Mathematical XXXXX.</strong> </p> <p>Work through XXX following steps to XXXXXX XXX parametric XXXXXXXXX where <em>x </em>is a function XX <em>t </em>and <em>y </em>XX a XXXXXXXX XX <em>t</em>. </p> <XX><li>XXXXX XXXX <em>t </em>XXXXXX <em>x</em>, XXXX plot <em>t </em>XXXXXX <em>y</em>. What XXXX XX XXXXXXXXXX should you use for each one XXXXX XX your XXXXXX? </li><li>Use your XXXXXXXXXX to XXXXXX a XXXXXXX for XXX model you XXXX chosen. XXXXX XXX ordered XXXXX into lists and have the XXXXXXXXXX create XXX line XX best fit XXX XXXX XXXXX. XXX XXXXXXX, XX your XXXX appears XX be XXXXXXXXXXX, you XXXX </li><li>XXXXX your XXXXX XXXXXXXXX: <XX><li><em>y</em>(<em>t</em>) = 2.8x+XX. <br> </li></XX></li></XX> <p>XXXX a XXXXX XX the form <em>y </em>= <em>ab<XXX>x</XXX> </em>XXXXX XXX XXXXXX XXXXXXX XX the calculator. </p> <p>· <em>x</em>(<em>t</em>) =X.XX^X - 1.XX^X - 3.XX - XX. </p> <XX>XXXX X: XXXXX XXXX model.</h1> <p>Plug in XXX values <em>t </em>= 0, X, 2, 3, XXX 4 XXXX XXXX parametric XXXXXXXXX and XXXXXX your XXXXXX XXX <em>x </em>XXX <em>y </em>in XXX table below. </p> <p> </p> <h2>Table 2</XX> <table> <tbody><tr> <td> <p><em>t</em> </p></td><td> <p><em>x</em> </p><p>(XXXXXXXXX) </p></td><td> <p><em>y</em> </p><p>(latitude) </p></td></tr> <tr> <td> <p>0 </p></td><td> <p>-92.X </p></td><td> <p>24.0 </p></td></tr> <tr> <td> <p>1 </p></td><td> <p>-95.8 </p></td><td> <p>26.8 </p></td></tr> <tr> <td> <p>2 </p></td><td> <p>-99.X </p></td><td> <p>XX.X </p></td></tr> <tr> <td> <p>3 </p></td><td> <p>-100.4 </p></td><td> <p>32.4 </p></td></tr> <tr> <td> <p>4 </p></td><td> <p>-96.X </p></td><td> <p>XX.2 </p></td></tr> </tbody></table> <p> </p> <p>Now graph the <em>x- </em>and <em>y</em>-XXXXXXXXXXX XXXX Table 1 XXXX XXXXX paper XXXXX one color, XXX XXXXX XXX <em>x- </em>and <em>y</em>-coordinates from XXXXX X onto XXX same XXXXX paper using a different XXXXX. You XXX either copy XXX XXXXX your graph here or XXXXXX it XXXXX with this XXXXXXXXX. </p> <p><img XXX="XXXX:///C:\XXXXX\abida\AppData\Local\Temp\msohtmlclip1\XX\clip_image005.XXX" width="337" height="203"> <XXX src="file:///X:\Users\XXXXX\AppData\Local\XXXX\XXXXXXXXXXXX\XX\clip_image007.XXX" width="XXX" XXXXXX="204"> </p> <p>XXXXXXX XXX XXXXX points with XXX XXXXXXXX XXXXXX XXX XXXXXX XXX following questions: </p> <ul><li>XXX does XXXX XXXXX compare XX XXX XXXXXX XXXX? </li><li>XXX XXX you choose XXX graph XXXXXX that you XXX? XXX you choose XXXX? Why or why not? </li><li>XX it possible to XXXXX <em>x</em>(<em>t</em>) for <em>t</em>, substitute it into <em>y</em>(<em>t</em>) to XXXXXXXXX the </li></XX> <p>XXX plot XXXX Table 2 XX XXXXXXXX XXXX XXXX XX XXXXX X. Besides that, XXXX XXX identitcal. </p> <p> </p> <p>I XXXXX the XXXXX graph XXXXXX because it XX a common graph XXXX is XXXXXX to observe </p> <p>XXX plot its XXXXXXXXXXXXXXX. XXX XXXXXX XX XXXX XX XXX XXXXX is XXXXXXXXXXXX XXX XXXXXX </p> <p>XXXXXXXXX, <em>t</em>, and XXXXX it as a XXXXXXXXXXX XXXXXXXX XXXX <em>x </em>XXX <em>y </em>XXXXXXX? XXX or XXX not? </p> <p>No, it XX XXX possible. XXXXXXX x(t) XXXXXXXX has a XXXXXXXXXXX of 3 (cube XXXX in y(t)). </p> <p>XXXXX, XXXXX XX XX mathematical XXXXXXXXXXXX XXXX can be done to XXXXXX XXX <XX> </p> <h2>XXXX it in:</h2> <p><br></p><p><XX></p><p><strong>Step X: Create a XXXXXXXXXXXX Model.</strong> </p> <p>Work through the following XXXXX XX create two parametric equations where <em>x </em>is a XXXXXXXX of <em>t </em>and <em>y </em>XX a XXXXXXXX XX <em>t</em>. </p> <XX><li>XXXXX XXXX <em>t </em>versus <em>x</em>, then XXXX <em>t </em>versus <em>y</em>. XXXX XXXX XX XXXXXXXXXX should you XXX XXX each XXX XXXXX on XXXX XXXXXX? </li><li>Use your calculator to XXXXXX a XXXXXXX XXX the XXXXX you have chosen. Enter XXX XXXXXXX XXXXX into XXXXX and have XXX calculator XXXXXX XXX XXXX XX XXXX fit for XXXX XXXXX. XXX example, if your XXXX XXXXXXX to be exponential, you will </li><li>Write your final equations: <ul><li><em>y</em>(<em>t</em>) = 2.XX+24. </li></XX></li></ul> <p>have a model XX the form <em>y </em>= <em>ab<sup>x</XXX> </em>XXXXX XXX ExpReg feature on the calculator. </p> <p>· <em>x</em>(<em>t</em>) =0.XX^X - 1.1x^X - X.1x - 92. </p> <XX>XXXX 4: Check your XXXXX.</XX> <p>XXXX in the XXXXXX <em>t </em>= 0, 1, X, 3, XXX X into your parametric equations XXX XXXXXX XXXX values for <em>x </em>XXX <em>y </em>in XXX table below. </p> <p> </p> <h2>Table X</XX> <table> <tbody><tr> <td><em>t</em> </td><td><em>x</em> <p>(XXXXXXXXX) </p></td><td><em>y</em> <p>(XXXXXXXX) </p></td></tr> <tr> <td>X </td><td>-XX.0 </td><td>XX.X </td></tr> <tr> <td>X </td><td>-XX.8 </td><td>XX.8 </td></tr> <tr> <td>X </td><td>-99.X </td><td>29.6 </td></tr> <tr> <td>3 </td><td>-XXX.4 </td><td>32.4 </td></tr> <tr> <td>X </td><td>-XX.X </td><td>XX.X </td></tr> </tbody></table> <p> </p> <p>XXX graph the <em>x- </em>XXX <em>y</em>-XXXXXXXXXXX from Table 1 XXXX XXXXX paper XXXXX XXX color, and graph XXX <em>x- </em>XXX <em>y</em>-coordinates XXXX XXXXX X onto the XXXX graph XXXXX using a different XXXXX. XXX may either XXXX XXX XXXXX XXXX XXXXX XXXX or XXXXXX it XXXXX XXXX XXXX XXXXXXXXX. </p> <p><img src="XXXX:///X:\XXXXX\XXXXX\XXXXXXX\XXXXX\XXXX\XXXXXXXXXXXX\01\clip_image005.jpg" width="XXX" XXXXXX="203"> <img src="file:///C:\XXXXX\abida\AppData\Local\Temp\XXXXXXXXXXXX\XX\XXXXXXXXXXXXX.jpg" width="XXX" XXXXXX="204"> </p> <p>XXXXXXX the model XXXXXX XXXX XXX XXXXXXXX points XXX XXXXXX XXX XXXXXXXXX questions: </p> <ul><li>How XXXX XXXX XXXXX compare XX the XXXXXX XXXX? </li><li>XXX XXX you XXXXXX the graph XXXXXX that you did? Did you choose XXXX? XXX or why XXX? </li><li>XX it possible XX solve <em>x</em>(<em>t</em>) XXX <em>t</em>, XXXXXXXXXX it XXXX <em>y</em>(<em>t</em>) XX eliminate XXX </li></XX> <p>The plot XXXX Table 2 is XXXXXXXX XXXX XXXX XX XXXXX 1. Besides that, XXXX XXX XXXXXXXXXX. </p> <p> </p> <p>I chose XXX cubic XXXXX XXXXXX because it XX a XXXXXX XXXXX that is XXXXXX XX observe </p> <p>and XXXX its characteristics. XXX XXXXXX is well as the XXXXX XX reproducible XXX easily </p> <p>parameter, <em>t</em>, XXX write it XX a rectangular XXXXXXXX XXXX <em>x </em>and <em>y </em>XXXXXXX? Why or why XXX? </p> <p>No, it XX XXX possible. XXXXXXX x(t) equation has a coefficient of X (cube root in y(t)). </p> <p>XXXXX, XXXXX is XX mathematical manipulation XXXX can XX XXXX XX remove the </p> <XX>XXXX it in:</XX> <p><XX></p>">
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