{"id":22823,"date":"2022-10-31T20:09:40","date_gmt":"2022-10-31T20:09:40","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=22823"},"modified":"2022-10-31T23:10:38","modified_gmt":"2022-10-31T23:10:38","slug":"o-museu-do-louvre","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=22823","title":{"rendered":"O Museu do Louvre"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_22823' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_22823' class='GTTabs_curr'><a  id=\"22823_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_22823' ><a  id=\"22823_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_22823'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>O Museu do Louvre \u00e9 um dos mais visitados do mundo. No ano 2001, recebeu a visita de \\(5\\,093\\,280\\) pessoas.<\/p>\n<p>A tabela apresenta o n\u00famero de visitantes, em tr\u00eas anos consecutivos.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/10\/8_Pag037-26.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"22825\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=22825\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/10\/8_Pag037-26.png\" data-orig-size=\"472,213\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag037-26\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/10\/8_Pag037-26.png\" class=\"aligncenter wp-image-22825\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/10\/8_Pag037-26-300x135.png\" alt=\"\" width=\"360\" height=\"162\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/10\/8_Pag037-26-300x135.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/10\/8_Pag037-26.png 472w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/a><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Qual \u00e9, de entre as express\u00f5es seguintes, a que est\u00e1 em nota\u00e7\u00e3o cient\u00edfica e \u00e9 a melhor aproxima\u00e7\u00e3o ao n\u00famero de visitantes do Museu do Louvre, em 2001?<br \/><strong>[A]<\/strong> \\(509 \\times {10^4}\\)\u00a0 \u00a0 \u00a0<strong>[B]<\/strong> \\(5,1 \\times {10^6}\\)\u00a0 \u00a0 \u00a0<strong>[C]<\/strong> \\(5,0 \\times {10^6}\\)\u00a0 \u00a0 \u00a0<strong>[D]<\/strong> \\(51 \\times {10^5}\\)<\/li>\n<li>Observa que o aumento do n\u00famero de visitantes, por ano, entre 2004 e 2006, \u00e9 constante. Determina o ano em que haver\u00e1 15,5 milh\u00f5es de visitantes, supondo que o aumento, nos anos seguintes, se mant\u00e9m constante.<br \/>Mostra como chegaste \u00e0 tua resposta.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_22823' onClick='GTTabs_show(1,22823)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_22823'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><\/p>\n<blockquote>\n<p>O Museu do Louvre \u00e9 um dos mais visitados do mundo. No ano 2001, recebeu a visita de \\(5\\,093\\,280\\) pessoas.<\/p>\n<p>A tabela apresenta o n\u00famero de visitantes, em tr\u00eas anos consecutivos.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/10\/8_Pag037-26.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"22825\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=22825\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/10\/8_Pag037-26.png\" data-orig-size=\"472,213\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag037-26\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/10\/8_Pag037-26.png\" class=\"aligncenter wp-image-22825\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/10\/8_Pag037-26-300x135.png\" alt=\"\" width=\"360\" height=\"162\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/10\/8_Pag037-26-300x135.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/10\/8_Pag037-26.png 472w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/a><\/p>\n<\/blockquote>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>\n<blockquote>Qual \u00e9, de entre as express\u00f5es seguintes, a que est\u00e1 em nota\u00e7\u00e3o cient\u00edfica e \u00e9 a melhor aproxima\u00e7\u00e3o ao n\u00famero de visitantes do Museu do Louvre, em 2001?<br \/><strong>[A]<\/strong> \\(509 \\times {10^4}\\)\u00a0 \u00a0 \u00a0<strong>[B]<\/strong> \\(5,1 \\times {10^6}\\)\u00a0 \u00a0 \u00a0<strong>[C]<\/strong> \\(5,0 \\times {10^6}\\)\u00a0 \u00a0 \u00a0<strong>[D]<\/strong> \\(51 \\times {10^5}\\)<\/blockquote>\n<\/li>\n<li>\n<blockquote>Observa que o aumento do n\u00famero de visitantes, por ano, entre 2004 e 2006, \u00e9 constante. Determina o ano em que haver\u00e1 15,5 milh\u00f5es de visitantes, supondo que o aumento, nos anos seguintes, se mant\u00e9m constante. Mostra como chegaste \u00e0 tua resposta.<\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>A express\u00e3o, que est\u00e1 em nota\u00e7\u00e3o cient\u00edfica e \u00e9 a melhor aproxima\u00e7\u00e3o ao n\u00famero de visitantes do Museu do Louvre, em 2001, \u00e9 <strong>[B]<\/strong> \\(5,1 \\times {10^6}\\), visto que \\(5,0 \\times {10^6} = 5\\,000\\,000\\) e \\(5,1 \\times {10^6} = 5\\,100\\,000\\).<br \/><br \/><\/li>\n<li>O aumento do n\u00famero de visitantes, por ano, entre 2004 e 2006, \u00e9 0,8 milh\u00f5es de visitantes.<br \/>Ora, comecemos por determinar o aumento do n\u00famero de visitantes necess\u00e1rio para atingir 15,5 milh\u00f5es de visitantes, em rela\u00e7\u00e3o ao n\u00famero de visitantes verificados em 2006: \\(\\left( {15,5 &#8211; 8,3} \\right)\\) milh\u00f5es, isto \u00e9, \\(7,2\\) milh\u00f5es. Portanto, ter\u00e3o de decorrer \\(7,2 \\div 0,8 = 9\\) anos a partir de 2006 para atingir os 15,5 milh\u00f5es de visitantes.<br \/>Assim, e nessa suposi\u00e7\u00e3o, ser\u00e1 no ano 2015 que haver\u00e1 15,5 milh\u00f5es de visitantes.<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<h6>Alternativa para a al\u00ednea b)<\/h6>\n<p>Atente \u00e0 constru\u00e7\u00e3o da tabela seguinte e repare nas duas sequ\u00eancias consideradas ((a<sub>n<\/sub>) e (v<sub>n<\/sub>)):<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 14.2857%;\">Anos &#8212; a<sub>n<\/sub><\/td>\n<td style=\"width: 14.2857%;\">2004 + (1-1)<\/td>\n<td style=\"width: 14.2857%;\">2004 + (2-1)<\/td>\n<td style=\"width: 14.2857%;\">2004 + (3-1)<\/td>\n<td style=\"width: 14.2857%;\">&#8230;<\/td>\n<td style=\"width: 14.2857%;\">2004 + (n-1)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 14.2857%;\">N.\u00ba de visitantes<br \/>(em milh\u00f5es)<\/td>\n<td style=\"width: 14.2857%;\">6,7<\/td>\n<td style=\"width: 14.2857%;\">7,5<\/td>\n<td style=\"width: 14.2857%;\">8,3<\/td>\n<td style=\"width: 14.2857%;\">\u00a0<\/td>\n<td style=\"width: 14.2857%;\">\u00a0<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 14.2857%;\">n<\/td>\n<td style=\"width: 14.2857%;\">1<\/td>\n<td style=\"width: 14.2857%;\">2<\/td>\n<td style=\"width: 14.2857%;\">3<\/td>\n<td style=\"width: 14.2857%;\">&#8230;<\/td>\n<td style=\"width: 14.2857%;\">n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 14.2857%;\">v<sub>n<\/sub><\/td>\n<td style=\"width: 14.2857%;\">6,7 + 0,8\u00d7(1-1)<\/td>\n<td style=\"width: 14.2857%;\">6,7 + 0,8\u00d7(2-1)<\/td>\n<td style=\"width: 14.2857%;\">6,7 + 0,8\u00d7(3-1)<\/td>\n<td style=\"width: 14.2857%;\">&#8230;<\/td>\n<td style=\"width: 14.2857%;\">6,7 + 0,8\u00d7(n-1)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Ora, comecemos por determinar \\(n\\), tal que \\({v_n} = 15,5\\):<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{v_n} = 15,5}&amp; \\Leftrightarrow &amp;{6,7 + 0,8 \\times \\left( {n &#8211; 1} \\right) = 15,5}\\\\{}&amp; \\Leftrightarrow &amp;{6,7 + 0,8 \\times n &#8211; 0,8 = 15,5}\\\\{}&amp; \\Leftrightarrow &amp;{0,8 \\times n = 15,5 + 0,8 &#8211; 6,7}\\\\{}&amp; \\Leftrightarrow &amp;{0,8 \\times n = 9,6}\\\\{}&amp; \\Leftrightarrow &amp;{n = \\frac{{9,6}}{{0,8}}}\\\\{}&amp; \\Leftrightarrow &amp;{n = 12}\\end{array}\\]<\/p>\n<p>Assim, e nessa suposi\u00e7\u00e3o, ser\u00e1 no ano \\(2004 + \\left( {12 &#8211; 1} \\right) = 2015\\) que haver\u00e1 15,5 milh\u00f5es de visitantes.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_22823' onClick='GTTabs_show(0,22823)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O Museu do Louvre \u00e9 um dos mais visitados do mundo. No ano 2001, recebeu a visita de \\(5\\,093\\,280\\) pessoas. A tabela apresenta o n\u00famero de visitantes, em tr\u00eas anos consecutivos.&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":22826,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,664],"tags":[424,143],"series":[],"class_list":["post-22823","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-numeros-reais","tag-8-o-ano","tag-notacao-cientifica"],"views":427,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/10\/Louvre_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22823","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=22823"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22823\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/22826"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=22823"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=22823"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=22823"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=22823"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}