{"id":10851,"date":"2014-11-08T15:55:03","date_gmt":"2014-11-08T20:55:03","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/ccpg1001\/?p=10851"},"modified":"2026-04-05T18:19:55","modified_gmt":"2026-04-05T23:19:55","slug":"s3eva2010ti_t1-ecuacion-verhulst","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/fp-s3eva10\/s3eva2010ti_t1-ecuacion-verhulst\/","title":{"rendered":"s3Eva2010TI_T1 Ecuaci\u00f3n Verhulst"},"content":{"rendered":"\n<p><strong>Ejercicio<\/strong>: <a href=\"https:\/\/blog.espol.edu.ec\/algoritmos101\/fp-3eva10\/3eva2010ti_t1-ecuacion-verhulst\/\" data-type=\"post\" data-id=\"2601\">3Eva2010TI_T1 Ecuaci\u00f3n Verhulst<\/a><\/p>\n\n\n\n<p>Para probar el ejercicio se usa po=1, a=0.5 b=0.02 y tiempo m\u00e1ximo=40<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> P(t) = \\frac{a P_0}{b P_0 + (a-b P_0)e^{-at}}<\/span>\n\n\n\n<p>con el algoritmo se puede observar:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>poblacion inicial p0:1\nfactor a:0.5\nfactor b:0.02\ncalcular en t:40\ntiempo:\n&#091;0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]\npi:\n&#091;1.0, 1.6070209244539886, 2.5434661610272977, 3.9338336459524355, 5.885057578381894, 8.417395145518748, 11.39009430586252, 14.494961881174662, 17.366232541771218, 19.73763290519436, 21.51998720327935, 22.766959376324014, 23.596257413785583, 24.129351687331045, 24.464588393188883, 24.67249666532522, 24.80032998711217, 24.878512232622807, 24.92617278160938, 24.95516943765841, 24.972789690449925, 24.983489042065916, 24.98998299475044, 24.99392342119231, 24.996314016127226, 24.99776420806526, 24.998643875922703, 24.999177451612496, 24.999501092725076, 24.99969739506529, 24.999816459955184, 24.999888677013956, 24.999932479077533, 24.999959046446833, 24.999975160398368, 24.999984934014144, 24.999990862015494, 24.99999445753143, 24.99999663832259, 24.999997961039472, 24.99999876330789]\n&gt;&gt;&gt;\n<\/code><\/pre>\n\n\n\n<p>que produce la siguiente gr\u00e1fica<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"480\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2014\/11\/EcuacionLogistica01.png\" alt=\"Ecuaci\u00f3n Log\u00edstica 01\" class=\"wp-image-18991\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Algoritmo en Python<\/h2>\n\n\n<div class=\"wp-block-syntaxhighlighter-code \"><pre class=\"brush: python; title: ; notranslate\" title=\"\">\n# 3Eva_IT2010_T1 Ecuaci\u00f3n Verhulst\nimport numpy as np\nimport matplotlib.pyplot as plt\n\ndef f_logistica(p0,a,b,t):\n    numerador = a*p0\n    denominador = b*p0+(a-b*p0)*np.exp(-a*t)\n    p = numerador\/denominador\n    return(p)\n\n# PROGRAMA ------\n# INGRESO\np0 = float(input(&quot;poblacion inicial p0:&quot;))\na  = float(input(&quot;factor a:&quot;))\nb  = float(input(&quot;factor b:&quot;))\nt  = float(input(&quot;calcular en t:&quot;))\n\n# PROCEDIMIENTO\nti = &#x5B;]\npi = &#x5B;]\ni = 0\nwhile i&lt;=t:\n    pi.append(f_logistica(p0,a,b,i))\n    ti.append(i)\n    i = i + 1\n\n# SALIDA\nnp.set_printoptions(precision=3)\nprint('tiempo:')\nprint(ti)\nprint('pi:')\nprint(pi)\n\n# grafica\nplt.plot(ti,pi)\nplt.xlabel('ti')\nplt.ylabel('pi')\nplt.title('ecuacion log\u00edstica')\nplt.show()\n<\/pre><\/div>\n\n\n<p><strong>Tarea<\/strong>: estimar el tiempo <strong>t<\/strong> cuando la poblaci\u00f3n se duplica<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ejercicio: 3Eva2010TI_T1 Ecuaci\u00f3n Verhulst Para probar el ejercicio se usa po=1, a=0.5 b=0.02 y tiempo m\u00e1ximo=40 con el algoritmo se puede observar: que produce la siguiente gr\u00e1fica Algoritmo en Python Tarea: estimar el tiempo t cuando la poblaci\u00f3n se duplica<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"wp-custom-template-entrada-fp-ejemplos","format":"standard","meta":{"footnotes":""},"categories":[138],"tags":[58,157],"class_list":["post-10851","post","type-post","status-publish","format-standard","hentry","category-fp-s3eva10","tag-ejemplos-python","tag-fundamentos-programacion"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/10851","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/users\/8043"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/comments?post=10851"}],"version-history":[{"count":5,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/10851\/revisions"}],"predecessor-version":[{"id":23718,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/10851\/revisions\/23718"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=10851"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=10851"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=10851"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}