{"id":95433,"date":"2017-01-18T12:17:19","date_gmt":"2017-01-18T14:17:19","guid":{"rendered":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/?p=95433"},"modified":"2026-05-19T19:44:20","modified_gmt":"2026-05-19T21:44:20","slug":"funcao-exponencial","status":"publish","type":"post","link":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/funcao-exponencial","title":{"rendered":"Fun\u00e7\u00e3o Exponencial"},"content":{"rendered":"<p>Uma<b>\u00a0fun\u00e7\u00e3o exponencial<\/b>\u00a0\u00e9 uma fun\u00e7\u00e3o matem\u00e1tica da forma f(x) = a &#8211; bx) ou f(x) = a . ekx, onde a vari\u00e1vel independente \\(x\\) est\u00e1 no expoente, a \u00e9 uma constante n\u00e3o nula (o coeficiente) e b \u00e9 uma base constante positiva (b&gt;0, b #1). Essas fun\u00e7\u00f5es modelam processos com crescimento ou decaimento r\u00e1pidos, como crescimento populacional, decaimento radioativo ou juros compostos, tipicamente apresentando uma curva que explode para cima ou se aproxima de zero.<\/p>\n<p>Ela modela crescimentos ou decrescimentos r\u00e1pidos, com gr\u00e1ficos que passam sempre pelo ponto ((0,1)\\). \u00c9 muito usada para juros compostos e popula\u00e7\u00f5es.<\/p>\n<p><b>Fun\u00e7\u00e3o Exponencial &#8211; O que \u00e9<\/b><\/p>\n<p>Uma\u00a0<strong>fun\u00e7\u00e3o exponencial<\/strong>\u00a0ocorre quando a vari\u00e1vel independente est\u00e1 no expoente de uma constante conhecida.<\/p>\n<p><strong>Exemplo:<\/strong>\u200b \u200b y(x) = 2 x<\/p>\n<p><strong>Exemplo:<\/strong>\u200b \u200b y(x) = 10 \u2212x<\/p>\n<p>Vamos estudar o comportamento das exponenciais positivas e negativas atrav\u00e9s do gr\u00e1fico.<\/p>\n<p>Este \u00e9 o gr\u00e1fico da fun\u00e7\u00e3o y(x) = 2<sup>x<\/sup><\/p>\n<p class=\"imagem\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-128036\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/funcao-exponencial-1.png\" alt=\"funcao-exponencial-1\" width=\"450\" height=\"328\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/funcao-exponencial-1.png 450w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/funcao-exponencial-1-300x219.png 300w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><\/p>\n<p>Vemos que o comportamento da fun\u00e7\u00e3o y(x) = 2 \u00e9 <strong>exponencial<\/strong>\u200b \u200be <strong>crescente<\/strong>\u200b, pois o x crescimento dela \u00e9 exponencial e o expoente da fun\u00e7\u00e3o \u00e9 positivo.<\/p>\n<p>Vamos ver o que acontece para as fun\u00e7\u00f5es de expoente negativo:<\/p>\n<p class=\"imagem\"><img decoding=\"async\" class=\"alignnone size-full wp-image-128037\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/funcao-exponencial-2.png\" alt=\"funcao-exponencial-2\" width=\"450\" height=\"356\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/funcao-exponencial-2.png 450w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/funcao-exponencial-2-300x237.png 300w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><\/p>\n<p>Esta exponencial \u00e9 decrescente\u200b \u200bpois seu expoente \u00e9 negativo.<\/p>\n<p><strong>Propriedades\u200b \u200bda\u200b \u200bfun\u00e7\u00e3o\u200b \u200bexponencial <\/strong><\/p>\n<p><strong>1) Injetividade:<\/strong>\u200b \u200bDizemos que uma fun\u00e7\u00e3o \u00e9 injetora quando todos os elementos do dom\u00ednio se associam a algum do contra-dom\u00ednio, ou seja, cada valor de x possui um valor de y associado pela fun\u00e7\u00e3o, como em y(x) = a , sendo a uma constante do x conjunto dos n\u00fameros naturais.<\/p>\n<p><strong>2) Sobrejetividade:<\/strong>\u200b \u200bA exponencial \u00e9 sobrejetora dado que para cada elemento do dom\u00ednio existe apenas um elemento do contra-dom\u00ednio associado pela fun\u00e7\u00e3o, isto \u00e9, existe apenas um valor de x para cada valor de y(x).<\/p>\n<p><strong>3) Bijetividade:<\/strong>\u200b \u200bUma fun\u00e7\u00e3o injetora e sobrejetora \u00e9 bijetora, ent\u00e3o, a exponencial \u00e9 bijetora.<\/p>\n<p><strong>Fonte:<\/strong>\u00a0Col\u00e9gio S\u00e3o Francisco\/Luisa Boccardo Burini<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Uma\u00a0fun\u00e7\u00e3o exponencial\u00a0\u00e9 uma fun\u00e7\u00e3o matem\u00e1tica da forma f(x) = a &#8211; bx) ou f(x) = a . ekx, onde a vari\u00e1vel independente \\(x\\) est\u00e1 no expoente, a \u00e9 uma constante n\u00e3o nula (o coeficiente) e b \u00e9 uma base constante positiva (b&gt;0, b #1). Essas fun\u00e7\u00f5es modelam processos com crescimento ou decaimento r\u00e1pidos, como crescimento [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[414],"tags":[],"class_list":["post-95433","post","type-post","status-publish","format-standard","hentry","category-matematica"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Fun\u00e7\u00e3o Exponencial - Portal S\u00e3o Francisco<\/title>\n<meta name=\"description\" content=\"Fun\u00e7\u00e3o Exponencial, Matem\u00e1tica, Gr\u00e1fico, Vari\u00e1vel Independente, Exemplo, Comportamento, Crescente, Decrescente, Propriedades, Fun\u00e7\u00e3o Exponencial\" \/>\n<meta name=\"robots\" content=\"noindex, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Fun\u00e7\u00e3o Exponencial - 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