{"id":7291,"date":"2012-01-01T16:01:14","date_gmt":"2012-01-01T16:01:14","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7291"},"modified":"2022-01-30T15:47:58","modified_gmt":"2022-01-30T15:47:58","slug":"num-parque-de-um-hipermercado","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7291","title":{"rendered":"Num parque de um hipermercado"},"content":{"rendered":"<p><ul id='GTTabs_ul_7291' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7291' class='GTTabs_curr'><a  id=\"7291_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7291' ><a  id=\"7291_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_7291'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Entre as 14 e as 15 horas param, num parque de um hipermercado, autom\u00f3veis \u00e0 raz\u00e3o de 12 autom\u00f3veis por hora (0,2 autom\u00f3veis por minuto). A seguinte f\u00f3rmula da estat\u00edstica pode ser usada para determinar a probabilidade de um carro chegar antes de decorrerem $t$ minutos, ap\u00f3s as 14 horas: $$P(t)=1-{{e}^{-0,2\\,t}}$$<\/p>\n<ol>\n<li>Qual a probabilidade de um carro chegar ao parque referido antes das 14 horas e 5 minutos?<\/li>\n<li>Qual a probabilidade de um carro chegar ao parque antes das 14 horas e 30 minutos?<\/li>\n<li>Use a calculadora para representar $P$ e determine quantos minutos s\u00e3o necess\u00e1rios para que a probabilidade atinja 75%.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7291' onClick='GTTabs_show(1,7291)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7291'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote><p>Entre as 14 e as 15 horas param, num parque de um hipermercado, autom\u00f3veis \u00e0 raz\u00e3o de 12 autom\u00f3veis por hora (0,2 autom\u00f3veis por minuto). A seguinte f\u00f3rmula da estat\u00edstica pode ser usada para determinar a probabilidade de um carro chegar antes de decorrerem $t$ minutos, ap\u00f3s as 14 horas: $$P(t)=1-{{e}^{-0,2\\,t}}$$<\/p><\/blockquote>\n<p>\u00ad<\/p>\n<ol>\n<li>A probabilidade de um carro chegar ao parque antes das 14 horas e 5 minutos \u00e9:\\[P(5) = 1 &#8211; {e^{ &#8211; 0,2 \\times 5}} = 1 &#8211; \\frac{1}{e} \\approx 0,632\\]\u00ad<\/li>\n<li>A probabilidade de um carro chegar ao parque antes das 14 horas e 30 minutos \u00e9:\\[P(30) = 1 &#8211; {e^{ &#8211; 0,2 \\times 30}} = 1 &#8211; {\\left( {\\frac{1}{e}} \\right)^6} \\approx 0,998\\]<\/li>\n<li>\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\/pag201-3a.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7292\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7292\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-3a.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=\"Janela\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-3a.png\" class=\"size-full wp-image-7292 aligncenter\" title=\"Janela\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-3a.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-3a.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-3a-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\/pag201-3b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7293\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7293\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-3b.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\/pag201-3b.png\" class=\"size-full wp-image-7293 aligncenter\" title=\"Gr\u00e1fico\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-3b.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-3b.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/pag201-3b-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>S\u00e3o necess\u00e1rios 7 minutos, aproximadamente, para que a probabilidade atinja 75%.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7291' onClick='GTTabs_show(0,7291)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Entre as 14 e as 15 horas param, num parque de um hipermercado, autom\u00f3veis \u00e0 raz\u00e3o de 12 autom\u00f3veis por hora (0,2 autom\u00f3veis por minuto). A seguinte f\u00f3rmula da estat\u00edstica pode&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21116,"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-7291","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":1223,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/12V2Pag201-3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7291","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=7291"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7291\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21116"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7291"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7291"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7291"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}