// Numbas version: finer_feedback_settings
{"name": "Geometric series - practical application", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["dur", "n", "m1", "m2", "m", "dayn"], "name": "Geometric series - practical application", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>a) Substitute in $n=\\var{dayn}$</p>\n<p>b) Substitute in $n=\\var{dur}$</p>\n<p>c) Use formula $S_n = \\frac{a_1(1-r^n)}{1-r}$ where $a_1$ is the first term and $r$ is the common ratio.</p>", "rulesets": {}, "parts": [{"integerPartialCredit": 0, "prompt": "<p>How long, to the nearest second, will Catherine's treatment be on day $\\var{dayn}$?</p>", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "precround({n}*{m}^{{dayn}-1},0)", "minValue": "precround({n}*{m}^{{dayn}-1},0)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "prompt": "<p>How long, to the nearest second, will Catherine's treatment be on day $\\var{dur}$?</p>", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "precround({n}*{m}^{{dur}-1},0)", "minValue": "precround({n}*{m}^{{dur}-1},0)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "prompt": "<p>How much time will she spend in total having this treatment for her eczema?</p>", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "precround(({n}*(1-{m}^{dur}))/(1-{m}),0)", "minValue": "precround(({n}*(1-{m}^{dur}))/(1-{m}),0)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>A hospital offers Catherine a $\\var{dur}$-day course of ultraviolet light therapy for her eczema. On day $n$ of the course, she is ot have $t_n$ seconds of treatment, where $t_n = \\var{n}\\times (\\simplify[all,fractionnumbers]{{m}})$$^{n-1}$</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "{dayn}<{dur}"}, "variables": {"m": {"definition": "1+1/m1", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "n": {"definition": "random(10..50)", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "dayn": {"definition": "random(5..30)", "templateType": "anything", "group": "Ungrouped variables", "name": "dayn", "description": ""}, "m1": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "m1", "description": ""}, "m2": {"definition": "random(4..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "m2", "description": ""}, "dur": {"definition": "random(10..50)", "templateType": "anything", "group": "Ungrouped variables", "name": "dur", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}]}]}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}]}