{"id":931,"date":"2025-09-13T16:39:37","date_gmt":"2025-09-13T22:39:37","guid":{"rendered":"https:\/\/portal.pronea.gt\/?p=931"},"modified":"2025-09-13T16:45:58","modified_gmt":"2025-09-13T22:45:58","slug":"temporary-title-790-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2","status":"publish","type":"post","link":"https:\/\/portal.pronea.gt\/?p=931","title":{"rendered":"La funci\u00f3n exponencial: entendiendo el crecimiento y el cambio"},"content":{"rendered":"<div id=\"cmsmasters_row_\" class=\"cmsmasters_row cmsmasters_color_scheme_default cmsmasters_row_top_default cmsmasters_row_bot_default cmsmasters_row_boxed\">\n<div class=\"cmsmasters_row_outer_parent\">\n<div class=\"cmsmasters_row_outer\">\n<div class=\"cmsmasters_row_inner\">\n<div class=\"cmsmasters_row_margin\">\n<div id=\"cmsmasters_column_\" class=\"cmsmasters_column one_first\">\n<div class=\"cmsmasters_column_inner\"><div class=\"cmsmasters_text\" data-animation=\"fadeIn\">\n<p data-start=\"2276\" data-end=\"2590\">La <strong data-start=\"2279\" data-end=\"2302\">funci\u00f3n exponencial<\/strong> es una de las m\u00e1s importantes en matem\u00e1ticas porque describe situaciones de crecimiento o decrecimiento acelerado. Est\u00e1 presente en fen\u00f3menos tan diversos como el aumento de una poblaci\u00f3n, la propagaci\u00f3n de enfermedades, el inter\u00e9s compuesto en finanzas o la desintegraci\u00f3n radiactiva.<\/p>\n<p data-start=\"2592\" data-end=\"2685\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f3a5.svg\" alt=\"\ud83c\udfa5\" \/> <strong data-start=\"2595\" data-end=\"2617\">Mira el video aqu\u00ed<\/strong><\/p>\n<iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/Pf0U940jQmM?si=ae14FVpUIaF45Q2I\" width=\"1120\" height=\"630\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe>\n<hr data-start=\"2687\" data-end=\"2690\" \/>\n<h2 data-start=\"2692\" data-end=\"2731\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4ca.svg\" alt=\"\ud83d\udcca\" \/> \u00bfQu\u00e9 es la funci\u00f3n exponencial?<\/h2>\n<p data-start=\"2732\" data-end=\"2777\">Una <strong data-start=\"2736\" data-end=\"2759\">funci\u00f3n exponencial<\/strong> tiene la forma:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-937\" src=\"https:\/\/portal.pronea.gt\/wp-content\/uploads\/2025\/09\/funcion_exponencial.png\" alt=\"F\u00f3rmula de la funci\u00f3n exponencial\" width=\"359\" height=\"31\" \/><\/p>\n<p data-start=\"2843\" data-end=\"2969\">Su caracter\u00edstica principal es que la variable aparece en el exponente, lo que genera un crecimiento o decrecimiento r\u00e1pido.<\/p>\n<hr data-start=\"2971\" data-end=\"2974\" \/>\n<h2 data-start=\"2976\" data-end=\"3006\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4c8.svg\" alt=\"\ud83d\udcc8\" \/> Representaci\u00f3n gr\u00e1fica<\/h2>\n<p data-start=\"3007\" data-end=\"3256\">La gr\u00e1fica de una funci\u00f3n exponencial muestra una curva ascendente (si <span class=\"katex\"><span class=\"katex-mathml\">a&gt;1a &gt; 1<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mrel\">&gt;<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span><\/span>) o descendente (si <span class=\"katex\"><span class=\"katex-mathml\">0&lt;a&lt;10 &lt; a &lt; 1<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">0<\/span><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span><\/span>).<br data-start=\"3122\" data-end=\"3125\" \/>Es continua y nunca toca el eje X, lo que la convierte en una herramienta clave para modelar procesos infinitos o de largo plazo.<\/p>\n<hr data-start=\"3258\" data-end=\"3261\" \/>\n<h2 data-start=\"3263\" data-end=\"3299\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f30d.svg\" alt=\"\ud83c\udf0d\" \/> Aplicaciones en la vida real<\/h2>\n<ul>\n<li data-start=\"3302\" data-end=\"3351\"><strong data-start=\"3302\" data-end=\"3315\">Econom\u00eda:<\/strong> c\u00e1lculo del inter\u00e9s compuesto. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4b0.svg\" alt=\"\ud83d\udcb0\" \/><\/li>\n<li data-start=\"3354\" data-end=\"3420\"><strong data-start=\"3354\" data-end=\"3367\">Biolog\u00eda:<\/strong> crecimiento poblacional y propagaci\u00f3n de virus. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f9ec.svg\" alt=\"\ud83e\uddec\" \/><\/li>\n<li data-start=\"3423\" data-end=\"3466\"><strong data-start=\"3423\" data-end=\"3434\">F\u00edsica:<\/strong> desintegraci\u00f3n radiactiva. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/269b.svg\" alt=\"\u269b\ufe0f\" \/><\/li>\n<li data-start=\"3469\" data-end=\"3524\"><strong data-start=\"3469\" data-end=\"3484\">Tecnolog\u00eda:<\/strong> an\u00e1lisis de algoritmos y procesos. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4bb.svg\" alt=\"\ud83d\udcbb\" \/><\/li>\n<\/ul>\n<hr data-start=\"3526\" data-end=\"3529\" \/>\n<h2 data-start=\"3531\" data-end=\"3558\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f393.svg\" alt=\"\ud83c\udf93\" \/> Aprender con PRONEA<\/h2>\n<p data-start=\"3559\" data-end=\"3816\">El <strong data-start=\"3562\" data-end=\"3617\">Programa Nacional de Educaci\u00f3n Alternativa \u2013PRONEA\u2013<\/strong> del Ministerio de Educaci\u00f3n de Guatemala acerca este conocimiento de manera clara y sencilla, demostrando que las matem\u00e1ticas no son complicadas, sino herramientas \u00fatiles para comprender el mundo.<\/p>\n<hr data-start=\"3818\" data-end=\"3821\" \/>\n<h2 data-start=\"3823\" data-end=\"3840\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/2705.svg\" alt=\"\u2705\" \/> Conclusi\u00f3n<\/h2>\n<p data-start=\"3841\" data-end=\"4050\">La <strong data-start=\"3844\" data-end=\"3867\">funci\u00f3n exponencial<\/strong> nos muestra c\u00f3mo crecen y cambian las cosas en la vida real. Comprenderla fortalece no solo las habilidades matem\u00e1ticas, sino tambi\u00e9n la capacidad de an\u00e1lisis en diferentes campos.<\/p>\n<p data-start=\"4052\" data-end=\"4103\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f449.svg\" alt=\"\ud83d\udc49\" \/> <strong data-start=\"4055\" data-end=\"4101\">PRONEA: la educaci\u00f3n que transforma vidas.<\/strong><\/p>\n<p><!-- \/wp:post-content --><\/p>\n<p><!-- wp:paragraph --><\/p>\n<p><!-- \/wp:paragraph --><\/p>\n<\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":933,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"image","meta":{"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"footnotes":""},"categories":[33,39],"tags":[],"class_list":["post-931","post","type-post","status-publish","format-image","has-post-thumbnail","hentry","category-matematicas","category-recursos","post_format-post-format-image"],"_links":{"self":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/931","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=931"}],"version-history":[{"count":6,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/931\/revisions"}],"predecessor-version":[{"id":939,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/931\/revisions\/939"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/media\/933"}],"wp:attachment":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=931"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=931"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=931"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}