// Numbas version: finer_feedback_settings
{"name": "Exponential population growth from formula", "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", "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 {objects} has a population, $P$, that can be described by the function $P = \\var{k} \\times \\var{a}^t&nbsp;$, where $t$ is the time in {timeperiod}.</p>", "advice": "<p>When $t=0$,</p>\n<p>$&nbsp; P = \\var{k} \\times \\var{a}^t = \\var{k} \\times \\var{a}^0 = 1$</p>\n<p>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>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"objectlist": {"name": "objectlist", "group": "Ungrouped variables", "definition": "['bacteria','ants','moths','viruses','mould spores']", "description": "", "templateType": "anything", "can_override": false}, "objectchoice": {"name": "objectchoice", "group": "Ungrouped variables", "definition": "random(0..4)", "description": "", "templateType": "anything", "can_override": false}, "object": {"name": "object", "group": "Ungrouped variables", "definition": "objectlist[objectchoice]", "description": "", "templateType": "anything", "can_override": false}, "timeperiodlist": {"name": "timeperiodlist", "group": "Ungrouped variables", "definition": "['days','weeks','months','years']", "description": "", "templateType": "anything", "can_override": false}, "timeperiodchoice": {"name": "timeperiodchoice", "group": "Ungrouped variables", "definition": "random(0..3)", "description": "", "templateType": "anything", "can_override": false}, "timeperiod": {"name": "timeperiod", "group": "Ungrouped variables", "definition": "timeperiodlist[timeperiodchoice]", "description": "", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(1..10000)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(11..50)/10", "description": "", "templateType": "anything", "can_override": false}, "time": {"name": "time", "group": "Ungrouped variables", "definition": "random(2..15)", "description": "", "templateType": "anything", "can_override": false}, "answer_raw": {"name": "answer_raw", "group": "Ungrouped variables", "definition": "k*a^time", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "round(answer_raw)", "description": "", "templateType": "anything", "can_override": false}, "objects": {"name": "objects", "group": "Ungrouped variables", "definition": "", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["objectlist", "objectchoice", "object", "timeperiodlist", "timeperiodchoice", "timeperiod", "k", "a", "time", "answer_raw", "answer", "objects"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the initial population, $P$, when $t$ = 0?</p>", "minValue": "{k}", "maxValue": "{k}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the 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, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}