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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 frXX XXX list that appears. </li><li>Select <em>Zoom to Storm </em>XXXXX the list XX view XXX full hurricane path. </li><li> </li><li>Make a table of XXX XXXXX’s XXXXXXXXXX and XXXXXXXX movement with respect XX XXXX. Hover over a XXXXXXXX point on XXX XXXX and XXXX the highlighted XXXX in XXX table XX XXX XXXX. Make this date <em>t </em>= 0. XXXX the position coordinates XXXX XXX XXXXX XXXX corner XX the map view XXX XXXXXX them in Table X. XXXXX XXXXXXXX measures XXXXX/south and longitude measures east/XXXX, XXX first XXXXXXXXXX will XX <em>y </em>and XXX XXXXXX XXXXXXXXXX XXXX XX <em>x</em>. XXX progress <XX> </li><li>XXXXXX this XXXXXXXXX into the XXXX Box. </li><li>XX you XXX XXX paste a copy XX XXXX XXXXX into the XXXXXXXXX, XX XXXX XX XXXX upload the graph into XXX XXXX Box. </li></ul> <p><u>XXXXXXXXXX XXXXXXXXX Tracks</u> </p> <p> </p> <XX>XXXX 2: Plot the hurricane XXXX.</h1> <p> <XXX src="XXXX:///X:\XXXXX\abida\AppData\Local\XXXX\XXXXXXXXXXXX\01\clip_image003.jpg" width="XXX" XXXXXX="202"><XX></p> <table> <tbody><tr> <td> <XX></td></tr> <tr> </tr> </tbody></table> <p> Take a XXXXXX shot XX XXX XXXXXXXXX XXXX XXX include it below: <br></p> <p>XXXXXXX the XXXX along the path. XXXX that you might XXXX to XXX the XXXXXX arrow XXXXXXX XX XXX XXXX information. In XXX table below, choose XXX record XXX XXXXX XXXX each day of the storm. XXXX each point <em>t </em>= 1, <em>t </em>= 2, XXX. </p> <p>Track XXX storm for a total of XX XXXXX five XXXX so that you have a minimum XX XXXX points in XXX table. XXX the XXXXXXX below to XXXX you XXXX XXX date, XXXXXXXX, XXX longitude. </p> <p> </p> <XX>XXXXX X</h2> <p> </p> <table> <tbody><tr> <td> <p>Date </p></td><td> <p><em>t</em> </p></td><td> <p><em>x</em> </p><p>(longitude) </p></td><td> <p><em>y</em> </p><p>(XXXXXXXX) </p></td></tr> <tr> <td> <p>Aug XX, 2017 </p></td><td> <p>0 </p></td><td> <p>-XX.XX </p></td><td> <p>24.XX </p></td></tr> <tr> <td> <p>Aug XX, 2017 </p></td><td> <p>X </p></td><td> <p>-XX.06 </p></td><td> <p>27.02 </p></td></tr> <tr> <td> <p>XXX XX, XXXX </p></td><td> <p>X </p></td><td> <p>-99.04 </p></td><td> <p>XX.XX </p></td></tr> <tr> <td> <p>XXX XX, XXXX </p></td><td> <p>X </p></td><td> <p>-101.69 </p></td><td> <p>32.XX </p></td></tr> <tr> <td> <p>Aug 19, XXXX </p></td><td> <p>4 </p></td><td> <p>-XX.61 </p></td><td> <p>XX.XX </p></td></tr> </tbody></table> <p> </p> <p><XXXXXX>XXXX 3: Create a XXXXXXXXXXXX XXXXX.</XXXXXX> </p> <p>XXXX XXXXXXX XXX XXXXXXXXX XXXXX to XXXXXX XXX XXXXXXXXXX equations XXXXX <em>x </em>XX a function XX <em>t </em>XXX <em>y </em>is a XXXXXXXX of <em>t</em>. </p> <XX><li>XXXXX plot <em>t </em>versus <em>x</em>, then plot <em>t </em>versus <em>y</em>. What kind XX XXXXXXXXXX should you use for XXXX one XXXXX on XXXX XXXXXX? </li><li>Use XXXX calculator XX create a XXXXXXX for XXX XXXXX you have chosen. Enter XXX XXXXXXX pairs into lists XXX have the XXXXXXXXXX XXXXXX XXX XXXX of XXXX fit for XXXX XXXXX. XXX XXXXXXX, XX XXXX XXXX XXXXXXX XX be exponential, you XXXX </li><li>Write XXXX XXXXX equations: <ul><li><em>y</em>(<em>t</em>) = 2.8x+24. <br> </li></XX></li></ul> <p>have a XXXXX of the XXXX <em>y </em>= <em>ab<sup>x</XXX> </em>XXXXX XXX XXXXXX XXXXXXX on XXX XXXXXXXXXX. </p> <p>· <em>x</em>(<em>t</em>) =X.4x^3 - 1.XX^X - 3.XX - 92. </p> <h1>XXXX X: XXXXX your model.</h1> <p>XXXX in XXX values <em>t </em>= X, X, 2, X, XXX X XXXX XXXX parametric equations XXX XXXXXX your XXXXXX XXX <em>x </em>and <em>y </em>in XXX table XXXXX. </p> <p> </p> <XX>XXXXX X</h2> <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>-XX.X </p></td><td> <p>XX.0 </p></td></tr> <tr> <td> <p>1 </p></td><td> <p>-XX.X </p></td><td> <p>26.8 </p></td></tr> <tr> <td> <p>2 </p></td><td> <p>-99.X </p></td><td> <p>29.X </p></td></tr> <tr> <td> <p>3 </p></td><td> <p>-XXX.4 </p></td><td> <p>XX.4 </p></td></tr> <tr> <td> <p>4 </p></td><td> <p>-XX.X </p></td><td> <p>35.X </p></td></tr> </tbody></table> <p> </p> <p>XXX XXXXX XXX <em>x- </em>and <em>y</em>-XXXXXXXXXXX XXXX Table 1 XXXX XXXXX XXXXX XXXXX one XXXXX, XXX graph XXX <em>x- </em>and <em>y</em>-coordinates from Table X onto XXX same XXXXX XXXXX XXXXX a different color. XXX XXX XXXXXX XXXX and XXXXX XXXX graph here or upload it XXXXX XXXX this XXXXXXXXX. </p> <p><img XXX="file:///X:\Users\XXXXX\AppData\XXXXX\Temp\XXXXXXXXXXXX\XX\XXXXXXXXXXXXX.jpg" width="337" height="203"> <img XXX="file:///X:\Users\abida\XXXXXXX\XXXXX\XXXX\XXXXXXXXXXXX\XX\clip_image007.XXX" width="XXX" XXXXXX="XXX"> </p> <p>XXXXXXX XXX XXXXX points with the XXXXXXXX points and answer XXX XXXXXXXXX questions: </p> <ul><li>XXX does your model compare XX the actual XXXX? </li><li>XXX XXX you choose the graph family that you XXX? XXX you choose XXXX? Why or why not? </li><li>Is it XXXXXXXX XX XXXXX <em>x</em>(<em>t</em>) for <em>t</em>, substitute it XXXX <em>y</em>(<em>t</em>) XX eliminate XXX </li></XX> <p>The plot XXXX Table X XX XXXXXXXX XXXX XXXX of XXXXX X. Besides that, XXXX XXX identitcal. </p> <p> </p> <p>I chose the cubic XXXXX XXXXXX XXXXXXX it XX a XXXXXX graph that is easier XX XXXXXXX </p> <p>XXX plot XXX characteristics. The choice XX well XX the XXXXX XX reproducible and XXXXXX </p> <p>parameter, <em>t</em>, and XXXXX it XX a rectangular XXXXXXXX XXXX <em>x </em>XXX <em>y </em>instead? XXX or XXX XXX? </p> <p>No, it is not possible. XXXXXXX x(t) XXXXXXXX XXX a XXXXXXXXXXX of X (cube XXXX in y(t)). </p> <p>XXXXX, XXXXX XX no XXXXXXXXXXXX XXXXXXXXXXXX XXXX XXX XX XXXX to XXXXXX XXX <XX> </p> <h2>XXXX it in:</h2> <p><br></p><p><br></p><p><strong>XXXX 3: XXXXXX a XXXXXXXXXXXX Model.</strong> </p> <p>Work through the XXXXXXXXX XXXXX to create two parametric XXXXXXXXX where <em>x </em>XX a function of <em>t </em>XXX <em>y </em>is a XXXXXXXX XX <em>t</em>. </p> <ul><li>XXXXX XXXX <em>t </em>versus <em>x</em>, XXXX plot <em>t </em>XXXXXX <em>y</em>. XXXX XXXX XX regression XXXXXX you XXX for XXXX one XXXXX XX XXXX graphs? </li><li>XXX XXXX XXXXXXXXXX XX create a XXXXXXX XXX the model you have chosen. Enter the XXXXXXX XXXXX XXXX lists and XXXX the calculator XXXXXX XXX XXXX of XXXX XXX XXX your model. For XXXXXXX, if XXXX path XXXXXXX XX be XXXXXXXXXXX, you XXXX </li><li>Write XXXX final XXXXXXXXX: <XX><li><em>y</em>(<em>t</em>) = X.XX+24. </li></XX></li></XX> <p>XXXX a model XX the XXXX <em>y </em>= <em>ab<XXX>x</XXX> </em>using the ExpReg XXXXXXX on XXX XXXXXXXXXX. </p> <p>· <em>x</em>(<em>t</em>) =X.XX^X - 1.1x^X - 3.1x - 92. </p> <h1>XXXX X: Check your XXXXX.</XX> <p>XXXX in XXX values <em>t </em>= X, X, X, X, and X XXXX your XXXXXXXXXX equations and insert your values for <em>x </em>XXX <em>y </em>in the table XXXXX. </p> <p> </p> <h2>Table 2</h2> <table> <tbody><tr> <td><em>t</em> </td><td><em>x</em> <p>(longitude) </p></td><td><em>y</em> <p>(latitude) </p></td></tr> <tr> <td>X </td><td>-92.X </td><td>24.0 </td></tr> <tr> <td>1 </td><td>-XX.X </td><td>XX.8 </td></tr> <tr> <td>2 </td><td>-XX.X </td><td>29.X </td></tr> <tr> <td>X </td><td>-XXX.X </td><td>XX.4 </td></tr> <tr> <td>4 </td><td>-96.4 </td><td>35.X </td></tr> </tbody></table> <p> </p> <p>XXX graph XXX <em>x- </em>and <em>y</em>-XXXXXXXXXXX from Table X onto graph XXXXX using one color, XXX graph the <em>x- </em>XXX <em>y</em>-coordinates from Table X XXXX the XXXX graph paper XXXXX a XXXXXXXXX color. You may XXXXXX copy and paste your XXXXX here or upload it along XXXX this XXXXXXXXX. </p> <p><img XXX="file:///C:\XXXXX\abida\AppData\XXXXX\XXXX\XXXXXXXXXXXX\XX\clip_image005.jpg" width="337" XXXXXX="XXX"> <img XXX="XXXX:///C:\XXXXX\XXXXX\AppData\XXXXX\Temp\msohtmlclip1\01\clip_image007.jpg" width="338" height="XXX"> </p> <p>XXXXXXX XXX XXXXX XXXXXX with XXX original points XXX XXXXXX the following XXXXXXXXX: </p> <ul><li>XXX XXXX XXXX XXXXX XXXXXXX to XXX XXXXXX XXXX? </li><li>XXX did you XXXXXX the graph family XXXX you did? Did you choose well? Why or XXX not? </li><li>XX it possible to solve <em>x</em>(<em>t</em>) for <em>t</em>, substitute it into <em>y</em>(<em>t</em>) to eliminate the </li></XX> <p>The XXXX from Table 2 is XXXXXXXX than that XX Table 1. Besides that, they are XXXXXXXXXX. </p> <p> </p> <p>I XXXXX XXX XXXXX XXXXX family because it XX a common graph XXXX is XXXXXX XX XXXXXXX </p> <p>and XXXX its characteristics. The XXXXXX is well XX the graph is reproducible and easily </p> <p>parameter, <em>t</em>, XXX XXXXX it as a rectangular equation XXXX <em>x </em>XXX <em>y </em>XXXXXXX? XXX or why XXX? </p> <p>No, it XX XXX possible. Because x(t) XXXXXXXX has a coefficient of 3 (XXXX XXXX in y(t)). </p> <p>Hence, there is no XXXXXXXXXXXX manipulation that can XX done to XXXXXX the </p> <XX>XXXX it in:</h2> <p><XX></p>">
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