{"id":7295,"date":"2012-01-01T18:01:14","date_gmt":"2012-01-01T18:01:14","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7295"},"modified":"2022-01-13T23:47:20","modified_gmt":"2022-01-13T23:47:20","slug":"propagacao-de-uma-doenca","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7295","title":{"rendered":"Propaga\u00e7\u00e3o de uma doen\u00e7a"},"content":{"rendered":"<p><ul id='GTTabs_ul_7295' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7295' class='GTTabs_curr'><a  id=\"7295_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7295' ><a  id=\"7295_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_7295'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A propaga\u00e7\u00e3o de uma certa doen\u00e7a segue um crescimento exponencial dado, em fun\u00e7\u00e3o do tempo, pela express\u00e3o: $$N={{e}^{0,77\\,t}}+6$$ em que $N$ representa o n\u00famero de pessoas contaminadas e $t$ o n\u00famero de anos decorridos desde o come\u00e7o de 1983, in\u00edcio da contagem do tempo ($t=0$).<\/p>\n<ol>\n<li>Determine o n\u00famero de pessoas que estariam contagiadas no in\u00edcio de 1980 e o que \u00e9 previs\u00edvel registar-se no come\u00e7o do ano de 1996, supondo que este modelo continua v\u00e1lido.<\/li>\n<li>Determine o ano e o m\u00eas em que, pela primeira vez, o n\u00famero de casos ultrapassa mil milh\u00f5es.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7295' onClick='GTTabs_show(1,7295)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7295'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>A propaga\u00e7\u00e3o de uma certa doen\u00e7a segue um crescimento exponencial dado, em fun\u00e7\u00e3o do tempo, pela express\u00e3o: $$N={{e}^{0,77\\,t}}+6$$ em que $N$ representa o n\u00famero de pessoas contaminadas e $t$ o n\u00famero de anos decorridos desde o come\u00e7o de 1983, in\u00edcio da contagem do tempo ($t=0$).<\/p>\n<\/blockquote>\n<ol>\n<li>\n<blockquote><p>Determine o n\u00famero de pessoas que estariam contagiadas no in\u00edcio de 1980 e o que \u00e9 previs\u00edvel registar-se no come\u00e7o do ano de 1996, supondo que este modelo continua v\u00e1lido.<\/p><\/blockquote>\n<\/li>\n<li>\n<blockquote><p>Determine o ano e o m\u00eas em que, pela primeira vez, o n\u00famero de casos ultrapassa mil milh\u00f5es.<\/p><\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00ad<\/p>\n<ol>\n<li>Os valores pedidos s\u00e3o, respetivamente, $N(-3)={{e}^{-0,77\\times 3}}+6\\approx 6$ e $N(13)={{e}^{0,77\\times 13}}+6\\approx 22254$ pessoas.<br \/>\n\u00ad<\/li>\n<li>Ora, $N&gt;{{10}^{9}}\\Leftrightarrow {{e}^{0,77\\,t}}&gt;{{10}^{9}}-6$. <a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-4a.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7296\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7296\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-4a.png\" data-orig-size=\"198,134\" 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;}\" data-image-title=\"Gr\u00e1fico\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-4a.png\" class=\"size-full wp-image-7296 aligncenter\" title=\"Gr\u00e1fico\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-4a.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-4a.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-4a-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><br \/>\nEsse n\u00famero \u00e9 alcan\u00e7ado no in\u00edcio de novembro de 2009.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7295' onClick='GTTabs_show(0,7295)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A propaga\u00e7\u00e3o de uma certa doen\u00e7a segue um crescimento exponencial dado, em fun\u00e7\u00e3o do tempo, pela express\u00e3o: $$N={{e}^{0,77\\,t}}+6$$ em que $N$ representa o n\u00famero de pessoas contaminadas e $t$ o n\u00famero&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19680,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,267],"tags":[427,268],"series":[],"class_list":["post-7295","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-funcoes-exponenciais-e-logaritmicas","tag-12-o-ano","tag-funcao-exponencial"],"views":3006,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/Higienizar.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7295","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=7295"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7295\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19680"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7295"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7295"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7295"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7295"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}