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{"name": "despeje de variable 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"d": {"description": "", "name": "d", "definition": "random(1..14#1)", "group": "Ungrouped variables", "templateType": "randrange"}, "k": {"description": "", "name": "k", "definition": "random(2..12#1)", "group": "Ungrouped variables", "templateType": "randrange"}, "c": {"description": "", "name": "c", "definition": "random(2..10#1)", "group": "Ungrouped variables", "templateType": "randrange"}, "m": {"description": "", "name": "m", "definition": "random(1.6..5#0.2)", "group": "Ungrouped variables", "templateType": "randrange"}}, "preamble": {"js": "", "css": ""}, "ungrouped_variables": ["k", "c", "m", "d"], "parts": [{"showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "marks": 0, "gaps": [{"showCorrectAnswer": true, "checkvariablenames": false, "scripts": {}, "variableReplacements": [], "showFeedbackIcon": true, "type": "jme", "variableReplacementStrategy": "originalfirst", "checkingtype": "absdiff", "expectedvariablenames": [], "marks": 1, "vsetrangepoints": 5, "checkingaccuracy": 0.001, "vsetrange": [0, 1], "answer": "(ln((1-y/{k})/{c})-{d})/{m}", "showpreview": true}], "showFeedbackIcon": true, "prompt": "<p>\\(x =\\)&nbsp;[[0]]</p>", "variableReplacements": [], "type": "gapfill"}], "rulesets": {}, "statement": "<p>Despeje \\(x\\) en la siguiente ecuaci&oacute;n:</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;\\(y=\\var{k}(1-\\var{c}e^{\\var{m}x+\\var{d}})\\)</p>", "name": "despeje de variable 2", "variable_groups": [], "advice": "<p style=\"text-align: left; padding-left: 60px;\">\\(y=\\var{k}(1-\\var{c}e^{\\var{m}x+\\var{d}})\\)</p>\n<p style=\"text-align: left;\">Trabajando desde afuera hacia adentro, dividimos a ambos lados por \\(\\var{k}\\) &nbsp;&nbsp;</p>\n<p style=\"text-align: left; padding-left: 60px;\">\\(\\frac{y}{\\var{k}}=1-\\var{c}e^{\\var{m}x+\\var{d}}\\)</p>\n<p style=\"text-align: left;\">Llevamos la variable \\(x\\) al lado izquierdo de la igualdad y movemos la variable \\(y\\) al lado derecho</p>\n<p style=\"text-align: left; padding-left: 60px;\">\\(\\var{c}e^{\\var{m}x+\\var{d}}=1-\\frac{y}{\\var{k}}\\)</p>\n<p style=\"text-align: left;\">Dividimos a ambos lados de la igualdad por \\(\\var{c}\\)</p>\n<p style=\"text-align: left; padding-left: 60px;\">\\(e^{\\var{m}x+\\var{d}}=\\frac{1-\\frac{y}{\\var{k}}}{\\var{c}}\\)</p>\n<p style=\"text-align: left;\">Aplicando $\\ln$ a ambos lados eliminamos \\(e\\) al lado izquierdo de la igualdad.&nbsp;</p>\n<p style=\"text-align: left; padding-left: 60px;\">\\(\\var{m}x+\\var{d}=ln\\left(\\frac{1-\\frac{y}{\\var{k}}}{\\var{c}}\\right)\\)</p>\n<p style=\"text-align: left;\">Restando \\(\\var{d}\\)&nbsp; a ambos lados de la igualdad</p>\n<p style=\"text-align: left; padding-left: 60px;\">\\(\\var{m}x=ln\\left(\\frac{1-\\frac{y}{\\var{k}}}{\\var{c}}\\right)-\\var{d}\\)</p>\n<p style=\"text-align: left;\">Y finalmente dividimos por \\(\\var{m}\\) para obtener</p>\n<p style=\"text-align: left; padding-left: 60px;\">\\(x=\\frac{ln\\left(\\frac{1-\\frac{y}{\\var{k}}}{\\var{c}}\\right)-\\var{d}}{\\var{m}}\\)</p>", "tags": [], "extensions": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Manipulation of an exponential function</p>"}, "type": "question", "contributors": [{"name": "Ricardo Monge", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/471/"}]}]}], "contributors": [{"name": "Ricardo Monge", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/471/"}]}