{"id":7286,"date":"2012-01-01T15:10:40","date_gmt":"2012-01-01T15:10:40","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7286"},"modified":"2022-01-30T15:28:49","modified_gmt":"2022-01-30T15:28:49","slug":"anestesiar-um-cao","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7286","title":{"rendered":"Anestesiar um c\u00e3o"},"content":{"rendered":"<p><ul id='GTTabs_ul_7286' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7286' class='GTTabs_curr'><a  id=\"7286_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7286' ><a  id=\"7286_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_7286'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Os veterin\u00e1rios usam pentobarbital de s\u00f3dio para anestesiar animais.<br \/>\nSuponha que a dose $d$ (em miligramas) necess\u00e1ria para anestesiar um c\u00e3o de 20 kg, durante o tempo $t$ (em horas) \u00e9 dada por: $$d(t)=600\\times {{2}^{\\frac{t}{4}}}$$<\/p>\n<ol>\n<li>Qual a dose necess\u00e1ria para anestesiar um c\u00e3o com o peso indicado durante 90 minutos?<br \/>\n(Apresente o resultado aproximado \u00e0s d\u00e9cimas)<\/li>\n<li>Durante quanto tempo (em horas e minutos) fica anestesiado um c\u00e3o de 20 kg se lhe for aplicada uma dosagem de $0,9$ gramas?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7286' onClick='GTTabs_show(1,7286)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7286'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote><p>Os veterin\u00e1rios usam pentobarbital de s\u00f3dio para anestesiar animais.<br \/>\nSuponha que a dose $d$ (em miligramas) necess\u00e1ria para anestesiar um c\u00e3o de 20 kg, durante o tempo $t$ (em horas) \u00e9 dada por: $$d(t)=600\\times {{2}^{\\frac{t}{4}}}$$<\/p><\/blockquote>\n<p>\u00ad<\/p>\n<ol>\n<li>A dose necess\u00e1ria para anestesiar um c\u00e3o com o peso indicado durante 90 minutos \u00e9: $d(1,5)=600\\times {{2}^{\\frac{1,5}{4}}}=600\\times {{2}^{\\frac{3}{8}}}\\approx 778,1$ miligramas.<br \/>\n\u00ad<\/li>\n<li>Ora, $$\\begin{array}{*{35}{l}} \u00a0\u00a0 d(t)=900 &amp; \\Leftrightarrow\u00a0 &amp; 600\\times {{2}^{\\frac{t}{4}}}=900\u00a0 \\\\ \u00a0\u00a0 {} &amp; \\Leftrightarrow\u00a0 &amp; {{2}^{\\frac{t}{4}}}=\\frac{3}{2}\u00a0 \\\\ \\end{array}$$ Recorrendo \u00e0 calculadora, podemos obter um valor aproximado da solu\u00e7\u00e3o:<br \/>\n<table class=\" aligncenter\" style=\"width: 400px;\" border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-2a.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7287\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7287\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-2a.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=\"Tabela\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-2a.png\" class=\"aligncenter size-full wp-image-7287\" title=\"Tabela\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-2a.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-2a.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-2a-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-2b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7288\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7288\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-2b.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\/pag201-2b.png\" class=\"aligncenter size-full wp-image-7288\" title=\"Gr\u00e1fico\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-2b.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-2b.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-2b-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Se lhe for aplicada uma dosagem de $0,9$ gramas, um c\u00e3o de $20$ kg fica anestesiado, aproximadamente, durante 2 horas e 20 minutos ($0,34\\times 60=20,4$).<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7286' onClick='GTTabs_show(0,7286)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Os veterin\u00e1rios usam pentobarbital de s\u00f3dio para anestesiar animais. Suponha que a dose $d$ (em miligramas) necess\u00e1ria para anestesiar um c\u00e3o de 20 kg, durante o tempo $t$ (em horas) \u00e9&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21114,"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-7286","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":3434,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/12V2Pag201-2-b_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7286","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=7286"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7286\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21114"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7286"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7286"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7286"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7286"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}