// 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": [{"parts": [{"showCorrectAnswer": true, "gaps": [{"precisionPartialCredit": 0, "precision": "3", "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "precisionType": "dp", "type": "numberentry", "correctAnswerStyle": "plain", "minValue": "(ln({k}/{a})-{c})/{m}", "marks": "2", "maxValue": "(ln({k}/{a})-{c})/{m}", "showCorrectAnswer": true, "correctAnswerFraction": false, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "scripts": {}}], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "gapfill", "prompt": "

Input your answer correct to three decimal places.

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\\(x = \\) [[0]]

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\\(\\var{k}=\\var{a}e^{\\var{m}x+{\\var{c}}}\\)

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\\(\\frac{\\var{k}}{\\var{a}}=e^{\\var{m}x+\\var{c}}\\)

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\\(ln\\left(\\frac{\\var{k}}{\\var{a}}\\right)=\\var{m}x+\\var{c}\\)

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\\(ln\\left(\\frac{\\var{k}}{\\var{a}}\\right)-\\var{c}=\\var{m}x\\)

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\\(\\frac{ln\\left(\\frac{\\var{k}}{\\var{a}}\\right)-\\var{c}}{\\var{m}}=x\\)

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Solve an exponential equation

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Given the equation \\(f(x)=\\var{a}e^{\\var{m}x+\\var{c}}\\)

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Determine the value for \\(x\\) that satisfies the relation \\(f(x)=\\var{k}\\)

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