// Numbas version: exam_results_page_options {"name": "Solve an exponential equation 2 (a e^(nx+c)=k)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Solve an exponential equation 2 (a e^(nx+c)=k)", "tags": [], "metadata": {"description": "

Solve an exponential equation

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

\n

Determine the value for \$$x\$$ that satisfies the equation: \$$\\var{a}e^{\\var{m}x+\\var{c}}=\\var{k}\$$

\n

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

\n

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

\n

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

\n

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

\n

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

", "rulesets": {}, "extensions": [], "variables": {"c": {"name": "c", "group": "Ungrouped variables", "definition": "random(0.1 .. 3#0.2)", "description": "", "templateType": "randrange"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(4 .. 20#1)", "description": "", "templateType": "randrange"}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(0.1 .. 1.5#0.1)", "description": "", "templateType": "randrange"}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(100 .. 150#1)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "c>0 or c<0 ", "maxRuns": 100}, "ungrouped_variables": ["a", "m", "c", "k"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

\$$x = \$$ [[0]]