// Numbas version: finer_feedback_settings
{"name": "Geometric series - practical application 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"js": "", "css": ""}, "ungrouped_variables": ["dur", "n", "m1", "m2", "m", "dayn"], "advice": "<p>The $n$<sup>th</sup> term in a geometric progression is given by $a_1 \\times r^{n-1}$ where $a_1$ is the first term and $r$ is the common ratio.&nbsp;</p>\n<p>We are given that the first term is $\\var{n}$ and the $\\var{dayn}$<sup>th</sup> term is $\\simplify{{n}*{m}^({dayn}-1)}$</p>\n<p>Hence we know that $r^{\\var{dayn}-1} = \\frac{\\simplify{{n}*{m}^({dayn}-1)}}{\\var{n}} =&nbsp;\\simplify{{m}^({dayn}-1)}$</p>\n<p>So we find that $r=\\var{m}$</p>\n<p></p>\n<p>If the pump were to extract air indefinitely, we look to the formula $S_n = \\frac{a_1}{1-r}$ to find $S_n = \\frac{\\var{n}}{1-\\var{m}} = \\simplify{{n}/(1-{m})}$</p>", "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "{dayn}<{dur}"}, "parts": [{"prompt": "<p>Determine the common ratio of the geometric series</p>", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "customMarkingAlgorithm": "", "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showCorrectAnswer": true, "marks": 1, "checkVariableNames": false, "valuegenerators": [], "customName": "", "answer": "{m}", "showPreview": true, "scripts": {}, "variableReplacements": [], "unitTests": [], "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "failureRate": 1, "answerSimplification": "all,fractionnumbers"}, {"prompt": "<p>Calculate the total amount of air that could be extracted from the bottle if the pump were to extract air indefinitely</p>", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "customMarkingAlgorithm": "", "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showCorrectAnswer": true, "marks": 1, "checkVariableNames": false, "valuegenerators": [], "customName": "", "answer": "{n}/(1-{m})", "showPreview": true, "scripts": {}, "variableReplacements": [], "unitTests": [], "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "failureRate": 1, "answerSimplification": "all"}], "tags": [], "statement": "<p>A pump is used to extract air from a bottle. The first operation of the pump extracts $\\var{n}$ cm$^3$ of air and subsequent extractions follow a geometric series. Extraction number $\\var{dayn}$ of the pump extracts $\\simplify{{n}*{m}^({dayn}-1)}$ cm$^3$ of air.</p>", "variables": {"dayn": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(3..9)", "name": "dayn"}, "m1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..5)", "name": "m1"}, "dur": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(10..50)", "name": "dur"}, "m": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "1-1/m1", "name": "m"}, "n": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(10..50)", "name": "n"}, "m2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(4..9)", "name": "m2"}}, "rulesets": {}, "functions": {}, "extensions": [], "name": "Geometric series - practical application 2", "type": "question", "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}