{"id":15720,"date":"2021-10-18T22:47:29","date_gmt":"2021-10-18T22:47:29","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/solutions-18-2\/"},"modified":"2021-11-07T01:36:50","modified_gmt":"2021-11-07T01:36:50","slug":"solutions-variation","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/solutions-variation\/","title":{"raw":"Solutions: Modeling Using Variation","rendered":"Solutions: Modeling Using Variation"},"content":{"raw":"<h2>Solutions to Odd-Numbered Exercises<\/h2>\r\n1.\u00a0The graph will have the appearance of a power function.\r\n\r\n3.\u00a0No. Multiple variables may jointly vary.\r\n\r\n5.\u00a0[latex]y=5{x}^{2}[\/latex]\r\n\r\n7.\u00a0[latex]y=10{x}^{3}[\/latex]\r\n\r\n9.\u00a0[latex]y=6{x}^{4}[\/latex]\r\n\r\n11.\u00a0[latex]y=\\frac{18}{{x}^{2}}[\/latex]\r\n\r\n13.\u00a0[latex]y=\\frac{81}{{x}^{4}}[\/latex]\r\n\r\n15.\u00a0[latex]y=\\frac{20}{\\sqrt[3]{x}}[\/latex]\r\n\r\n17.\u00a0[latex]y=10xzw[\/latex]\r\n\r\n19.\u00a0[latex]y=10x\\sqrt{z}[\/latex]\r\n\r\n21.\u00a0[latex]y=4\\frac{xz}{w}[\/latex]\r\n\r\n23.\u00a0[latex]y=40\\frac{xz}{\\sqrt{w}{t}^{2}}[\/latex]\r\n\r\n25.\u00a0[latex]y=256[\/latex]\r\n\r\n27.\u00a0[latex]y=6[\/latex]\r\n\r\n29.\u00a0[latex]y=6[\/latex]\r\n\r\n31.\u00a0[latex]y=27[\/latex]\r\n\r\n33.\u00a0[latex]y=3[\/latex]\r\n\r\n35.\u00a0[latex]y=18[\/latex]\r\n\r\n37.\u00a0[latex]y=90[\/latex]\r\n\r\n39.\u00a0[latex]y=\\frac{81}{2}[\/latex]\r\n\r\n41.\u00a0[latex]y=\\frac{3}{4}{x}^{2}[\/latex]\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03010806\/CNX_Precalc_Figure_03_09_2012.jpg\" alt=\"Graph of y=3\/4(x^2).\" \/>\r\n\r\n43.\u00a0[latex]y=\\frac{1}{3}\\sqrt{x}[\/latex]\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03010806\/CNX_Precalc_Figure_03_09_2032.jpg\" alt=\"Graph of y=1\/3sqrt(x).\" \/>\r\n\r\n45.\u00a0[latex]y=\\frac{4}{{x}^{2}}[\/latex]\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03010807\/CNX_Precalc_Figure_03_09_2052.jpg\" alt=\"Graph of y=4\/(x^2).\" \/>\r\n\r\n47.\u00a01.89 years\r\n\r\n49.\u00a00.61 years\r\n\r\n51.\u00a03 seconds\r\n\r\n53.\u00a048 inches\r\n\r\n55.\u00a049.75 pounds\r\n\r\n57.\u00a033.33 amperes\r\n\r\n59.\u00a02.88 inches","rendered":"<h2>Solutions to Odd-Numbered Exercises<\/h2>\n<p>1.\u00a0The graph will have the appearance of a power function.<\/p>\n<p>3.\u00a0No. Multiple variables may jointly vary.<\/p>\n<p>5.\u00a0[latex]y=5{x}^{2}[\/latex]<\/p>\n<p>7.\u00a0[latex]y=10{x}^{3}[\/latex]<\/p>\n<p>9.\u00a0[latex]y=6{x}^{4}[\/latex]<\/p>\n<p>11.\u00a0[latex]y=\\frac{18}{{x}^{2}}[\/latex]<\/p>\n<p>13.\u00a0[latex]y=\\frac{81}{{x}^{4}}[\/latex]<\/p>\n<p>15.\u00a0[latex]y=\\frac{20}{\\sqrt[3]{x}}[\/latex]<\/p>\n<p>17.\u00a0[latex]y=10xzw[\/latex]<\/p>\n<p>19.\u00a0[latex]y=10x\\sqrt{z}[\/latex]<\/p>\n<p>21.\u00a0[latex]y=4\\frac{xz}{w}[\/latex]<\/p>\n<p>23.\u00a0[latex]y=40\\frac{xz}{\\sqrt{w}{t}^{2}}[\/latex]<\/p>\n<p>25.\u00a0[latex]y=256[\/latex]<\/p>\n<p>27.\u00a0[latex]y=6[\/latex]<\/p>\n<p>29.\u00a0[latex]y=6[\/latex]<\/p>\n<p>31.\u00a0[latex]y=27[\/latex]<\/p>\n<p>33.\u00a0[latex]y=3[\/latex]<\/p>\n<p>35.\u00a0[latex]y=18[\/latex]<\/p>\n<p>37.\u00a0[latex]y=90[\/latex]<\/p>\n<p>39.\u00a0[latex]y=\\frac{81}{2}[\/latex]<\/p>\n<p>41.\u00a0[latex]y=\\frac{3}{4}{x}^{2}[\/latex]<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03010806\/CNX_Precalc_Figure_03_09_2012.jpg\" alt=\"Graph of y=3\/4(x^2).\" \/><\/p>\n<p>43.\u00a0[latex]y=\\frac{1}{3}\\sqrt{x}[\/latex]<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03010806\/CNX_Precalc_Figure_03_09_2032.jpg\" alt=\"Graph of y=1\/3sqrt(x).\" \/><\/p>\n<p>45.\u00a0[latex]y=\\frac{4}{{x}^{2}}[\/latex]<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03010807\/CNX_Precalc_Figure_03_09_2052.jpg\" alt=\"Graph of y=4\/(x^2).\" \/><\/p>\n<p>47.\u00a01.89 years<\/p>\n<p>49.\u00a00.61 years<\/p>\n<p>51.\u00a03 seconds<\/p>\n<p>53.\u00a048 inches<\/p>\n<p>55.\u00a049.75 pounds<\/p>\n<p>57.\u00a033.33 amperes<\/p>\n<p>59.\u00a02.88 inches<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-15720\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Precalculus. <strong>Authored by<\/strong>: Jay Abramson, et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":167848,"menu_order":12,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Precalculus\",\"author\":\"Jay Abramson, et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-15720","chapter","type-chapter","status-publish","hentry"],"part":15618,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15720","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/users\/167848"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15720\/revisions"}],"predecessor-version":[{"id":16049,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15720\/revisions\/16049"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/parts\/15618"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15720\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/media?parent=15720"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapter-type?post=15720"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/contributor?post=15720"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/license?post=15720"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}