// Numbas version: exam_results_page_options
{"name": "Exponential population growth from formula with inverse", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Exponential population growth from formula with inverse", "tags": [], "metadata": {"description": "<p>Students are given an exponential equation and asked to evaluate it at two points.</p>\n<p>The constants in the exponential are randomised.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>A population of bacteria has a population, $P$, that can be described by the function $P = \\var{k} \\times \\var{a}^t $, where $t$ is the time in {timeperiod}.</p>", "advice": "<p>a) When $t=0$,</p>\n<p>$&nbsp; P = \\var{k} \\times \\var{a}^t = \\var{k} \\times \\var{a}^0 = 1$</p>\n<p></p>\n<p>b) When $t = \\var{time}$,</p>\n<p>$P = \\var{k} \\times \\var{a}^\\var{time} = \\var{answer_raw}$</p>\n<p>When this is rounded to the nearest whole number, we get</p>\n<p>$P = \\var{answer}$</p>\n<p></p>\n<p>c) We need to take $t = -2$,</p>\n<p>$P = \\var{k} \\times \\var{a}^{-2} = \\var{ansc}$,</p>\n<p>When this is rounded to the nearest whole number, we get</p>\n<p>$P = \\var{ansc_r}$.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "1 + random(10..70)/100", "description": "", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(1..10000)", "description": "", "templateType": "anything", "can_override": false}, "timeperiod": {"name": "timeperiod", "group": "Ungrouped variables", "definition": "timeperiodlist[timeperiodchoice]", "description": "", "templateType": "anything", "can_override": false}, 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"anything", "can_override": false}, "ansc_r": {"name": "ansc_r", "group": "Ungrouped variables", "definition": "round(ansc)", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "round(answer_raw)", "description": "", "templateType": "anything", "can_override": false}, "answer_raw": {"name": "answer_raw", "group": "Ungrouped variables", "definition": "k*a^time", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "k", "timeperiod", "timeperiodchoice", "timeperiodlist", "time", "l", "k_over_l", "ansc", "ansc_r", "answer", "answer_raw"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": true, "customName": "Part a)", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, 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population, $P$, when $t = \\var{time}$ {timeperiod}</p>\n<p>Round your answer to the nearest whole number.</p>", "minValue": "round({k}*{a}^{time})", "maxValue": "round({k}*{a}^{time})", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "<p>What was the population, $P$, 2 {timeperiod} ago</p>\n<p>Round your answer to the nearest whole number.</p>\n<p>[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": 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