// Numbas version: exam_results_page_options
{"name": "Solve an exponential equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "<p style=\"text-align: center;\">\\(\\var{k}=\\var{a}e^{\\var{m}x+{\\var{c}}}\\)</p>\n<p style=\"text-align: center;\">\\(\\frac{\\var{k}}{\\var{a}}=e^{\\var{m}x+\\var{c}}\\)</p>\n<p style=\"text-align: center;\">\\(ln\\left(\\frac{\\var{k}}{\\var{a}}\\right)=\\var{m}x+\\var{c}\\)</p>\n<p style=\"text-align: center;\">\\(ln\\left(\\frac{\\var{k}}{\\var{a}}\\right)-\\var{c}=\\var{m}x\\)</p>\n<p style=\"text-align: center;\">\\(\\frac{ln\\left(\\frac{\\var{k}}{\\var{a}}\\right)-\\var{c}}{\\var{m}}=x\\)</p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Solve an exponential equation</p>"}, "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["a", "m", "c", "k"], "variable_groups": [], "name": "Solve an exponential equation", "functions": {}, "statement": "<p>Given the equation \\(f(x)=\\var{a}e^{\\var{m}x+\\var{c}}\\)</p>\n<p>Determine the value for \\(x\\) that satisfies the relation \\(f(x)=\\var{k}\\)</p>", "tags": [], "rulesets": {}, "parts": [{"marks": 0, "prompt": "<p>Input your answer correct to three decimal places.</p>\n<p style=\"padding-left: 30px;\">\\(x = \\) [[0]]</p>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "type": "gapfill", "gaps": [{"mustBeReducedPC": 0, "precisionPartialCredit": 0, "maxValue": "(ln({k}/{a})-{c})/{m}", "precision": "3", "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerFraction": false, "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "allowFractions": false, "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "showPrecisionHint": false, "marks": "2", "scripts": {}, "variableReplacements": [], "showFeedbackIcon": true, "minValue": "(ln({k}/{a})-{c})/{m}"}]}], "variables": {"a": {"templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": "", "definition": "random(4..20#1)"}, "c": {"templateType": "randrange", "group": "Ungrouped variables", "name": "c", "description": "", "definition": "random(0.1..3#0.2)"}, "m": {"templateType": "randrange", "group": "Ungrouped variables", "name": "m", "description": "", "definition": "random(0.1..1.5#0.1)"}, "k": {"templateType": "randrange", "group": "Ungrouped variables", "name": "k", "description": "", "definition": "random(100..150#1)"}}, "variablesTest": {"maxRuns": 100, "condition": "c>0 or c<0 "}, "extensions": [], "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}