// Numbas version: exam_results_page_options
{"name": "Exponential increase", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Exponential increase", "type": "question", "statement": "<p>A comic book collector bought a comic book&nbsp;for {pounds(ori)}&nbsp;when it came out.</p>\n<p>Now, {years} years later, its value has increased to {pounds(new)}.&nbsp;</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"new": {"group": "Ungrouped variables", "description": "<p>The new comic book value.</p>", "templateType": "anything", "name": "new", "definition": "precround(ori * ((100+perc)/100)^years, 2)"}, "years": {"group": "Ungrouped variables", "description": "<p>Number of years.</p>", "templateType": "anything", "name": "years", "definition": "random(3..6)"}, "ori": {"group": "Ungrouped variables", "description": "<p>The old comic book price.</p>", "templateType": "anything", "name": "ori", "definition": "random(3..15) + 0.99"}, "perc": {"group": "Ungrouped variables", "description": "<p>Percentage increase per year.</p>", "templateType": "anything", "name": "perc", "definition": "random(5..15 #0.1)"}, "x": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "x", "definition": "precround(root(new/ori, years),4)"}}, "extensions": [], "functions": {"pounds": {"parameters": [["n", "number"]], "type": "string", "language": "jme", "definition": "currency(n,\"\u00a3\",\"p\")"}}, "tags": ["increase", "percentages", "taxonomy"], "variable_groups": [], "parts": [{"scripts": {}, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "stepsPenalty": "1", "gaps": [{"correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "precisionPartialCredit": 0, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "precision": "1", "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "maxValue": "perc", "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReduced": false, "minValue": "perc", "variableReplacements": [], "marks": "2", "showPrecisionHint": false, "strictPrecision": false, "showCorrectAnswer": true}], "showCorrectAnswer": true, "prompt": "<p>What was the average percentage increase per year?&nbsp;</p>\n<p>[[0]]% increase per year &nbsp; &nbsp; &nbsp; &nbsp;<em><small>&nbsp;Round your answer to 1 decimal place.</small></em></p>", "steps": [{"scripts": {}, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "showCorrectAnswer": true, "prompt": "<p>Let $x$ denote the decimal multiplier. Then</p>\n<p>\\[ \\var{ori} \\times x^\\var{years} = \\var{new} \\]</p>", "type": "information"}], "type": "gapfill"}], "ungrouped_variables": ["ori", "new", "perc", "years", "x"], "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Work out the average percentage increase per year in price of an item, given two prices several years apart.</p>"}, "preamble": {"css": "", "js": ""}, "advice": "<p>Let $x$ be the decimal multiplier, then</p>\n<p>\\[ <br/>\\begin{align} <br/>\\var{dpformat(ori,2)} \\times x^\\var{years} &amp;= \\var{dpformat(new,2)} \\\\ <br/>x^\\var{years} &amp;= \\var{precround(new/ori,4)}&nbsp;\\\\ <br/>x &amp;= \\sqrt[\\var{years}]{\\var{precround(new/ori,4)}} \\\\<br/>&amp;= \\var{x} \\text{.} \\end{align}\\]</p>\n<p>To find the percentage change, we multiply $x$ by 100.</p>\n<p>\\[ &nbsp;x \\times 100 = \\var{precround(x*100, 1)} \\% \\]</p>\n<p>The price has changed by $\\var{precround(x*100, 1)}$% each year. To find the percentage increase, we subtract $100$, to give an answer of $&nbsp;\\var{perc}$%.</p>", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}]}