{"id":6007,"date":"2024-05-12T21:28:49","date_gmt":"2024-05-13T00:28:49","guid":{"rendered":"https:\/\/xequematenem.com.br\/blog\/?p=6007"},"modified":"2024-10-03T09:50:34","modified_gmt":"2024-10-03T12:50:34","slug":"questao-145-enem-ppl-2021","status":"publish","type":"post","link":"https:\/\/xequematenem.com.br\/blog\/questao-145-enem-ppl-2021\/","title":{"rendered":"Quest\u00e3o 145 &#8211; Enem PPL 2021"},"content":{"rendered":"\n<p class=\"has-text-align-center wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Um casal decidiu aplicar em um fundo de investimentos que tem uma taxa de rendimento de <strong>0,8% ao m\u00eas,<\/strong> num regime de capitaliza\u00e7\u00e3o composta.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>O valor final F a ser resgatado, depois de n meses, a uma taxa de rendimento mensal x,<\/strong> \u00e9 dado pela express\u00e3o alg\u00e9brica<strong> F = C (1 + x)<\/strong><strong><sup>n<\/sup><\/strong><strong>, em que C representa o capital inicial aplicado.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">O casal planeja manter a aplica\u00e7\u00e3o pelo tempo necess\u00e1rio para que o capital inicial de<strong> R$ 100 000,00 duplique, sem outros dep\u00f3sitos ou retiradas.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Fazendo uso da tabela, o casal pode determinar esse n\u00famero de meses.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"444\" height=\"380\" src=\"https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2024\/05\/image-16.png\" alt=\"\" class=\"wp-image-6008\" title=\"\" srcset=\"https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2024\/05\/image-16.png 444w, https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2024\/05\/image-16-300x257.png 300w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Para atender ao seu planejamento, o n\u00famero de meses determinado pelo casal \u00e9<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A) 156.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B) 125.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C) 100.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D) 10.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">E) 1,5.<\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size wp-block-paragraph\"><strong>Resolu\u00e7\u00e3o<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Se queremos que F seja p dobro de C e a taxa \u00e9 0,8%=0,008 temos<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2C = C(1 + 0,008)<sup>n<\/sup>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ou seja<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2 = 1,008<sup>n<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Tirando o log dos dois lados temos<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">log2 = log1,008<sup>n<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pela propriedade de log<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">log2 = n.log1,008<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">substituindo os valores dados na tabela<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">0,3 = n.0,003<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">n = 0,3\/0,003&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">n = 100<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Alternativa C<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Assista \u00e0 resolu\u00e7\u00e3o com mais detalhes no v\u00eddeo abaixo!<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe title=\"Quest\u00e3o 145 - Caderno Azul | Logaritmo | MATEM\u00c1TICA ENEM PPL 2021\" width=\"800\" height=\"450\" data-src=\"https:\/\/www.youtube.com\/embed\/KEi0_peA4oA?list=PLrzB-zHlu3aAqV-y3sXkQB832I6nvGDZn\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" data-load-mode=\"1\"><\/iframe>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Um casal decidiu aplicar em um fundo de investimentos que tem uma taxa de rendimento de 0,8% ao m\u00eas, num regime de capitaliza\u00e7\u00e3o composta. O valor final F a ser resgatado, depois de n meses, a uma taxa de rendimento mensal x, \u00e9 dado pela express\u00e3o alg\u00e9brica F = C (1 + x)n, em que [&hellip;]<\/p>\n","protected":false},"author":11,"featured_media":6008,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[87,100],"tags":[],"area-do-conhecimento":[132,118],"assunto":[53],"class_list":["post-6007","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-questoes-ppl","category-2021-questoes-ppl","area-do-conhecimento-matematica","area-do-conhecimento-matematica-e-suas-tecnologias","assunto-logaritmo"],"_links":{"self":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts\/6007","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/comments?post=6007"}],"version-history":[{"count":1,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts\/6007\/revisions"}],"predecessor-version":[{"id":18837,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts\/6007\/revisions\/18837"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/media\/6008"}],"wp:attachment":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/media?parent=6007"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/categories?post=6007"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/tags?post=6007"},{"taxonomy":"area-do-conhecimento","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/area-do-conhecimento?post=6007"},{"taxonomy":"assunto","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/assunto?post=6007"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}