// Numbas version: exam_results_page_options
{"name": "Ida's copy of Cumulative percent decrease", "extensions": ["random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Ida's copy of Cumulative percent decrease", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Given the original price of a smartphone and the rate at which it decreases, calculate its price after a given number of months. In the second part, calculate the time remaining until the price goes below a&nbsp;certain point.</p>"}, "parts": [{"prompt": "<p>Hvor mye koster smartphonen etter $1$ m&aring;ned?</p>\n<p>Svar:&nbsp;[[0]]</p>", "marks": 0, "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "gapfill", "variableReplacements": [], "steps": [{"prompt": "<p>The original price of the phone is $&pound;\\var{price}$ and we are told that the price decreases&nbsp;by $\\var{perc}$% every month.</p>\n<p></p>", "marks": 0, "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "information", "variableReplacements": [], "scripts": {}, "variableReplacementStrategy": "originalfirst"}, {"correctAnswerFraction": false, "marks": "0.5", "showFeedbackIcon": true, "prompt": "<p>What is the decimal multiplier for the decrease in the smartphones each month?</p>", "correctAnswerStyle": "plain", "maxValue": "1-{perc}/100", "scripts": {}, "type": "numberentry", "variableReplacements": [], "minValue": "1-{perc}/100", "mustBeReducedPC": 0, "showCorrectAnswer": true, "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacementStrategy": "originalfirst"}, {"marks": "0.5", "allowFractions": false, "precision": "2", "correctAnswerStyle": "plain", "maxValue": "{price}*(1-{perc}/100)", "precisionMessage": "<p>Round your answer to $2$ decimal places.</p>", "scripts": {}, "variableReplacements": [], "precisionType": "dp", "mustBeReduced": false, "correctAnswerFraction": false, "showFeedbackIcon": true, "prompt": "<p>Multiply the original&nbsp;price by the decimal multiplier to obtain the price after 1 month.</p>", "type": "numberentry", "showPrecisionHint": true, "minValue": "{price}*(1-{perc}/100)", "mustBeReducedPC": 0, "showCorrectAnswer": true, "strictPrecision": false, "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"]}], "gaps": [{"correctAnswerFraction": false, "marks": "2", "allowFractions": false, "precision": "1", "type": "numberentry", "correctAnswerStyle": "plain", "maxValue": "precround(price*((100-perc)/100), 2)", "precisionMessage": "<p>Avrundning til $1$ desimal.</p>", "scripts": {}, "precisionPartialCredit": 0, "showPrecisionHint": true, "variableReplacements": [], "minValue": "precround(price*((100-perc)/100), 2)", "mustBeReducedPC": 0, "showCorrectAnswer": true, "strictPrecision": false, "showFeedbackIcon": true, "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacementStrategy": "originalfirst"}], "scripts": {}, "stepsPenalty": 0, "variableReplacementStrategy": "originalfirst"}, {"prompt": "<p>Hvor mye koster smartphonen etter $5$ m&aring;neder?</p>\n<p><span style=\"text-decoration: underline;\">Uppst&auml;llning av utr&auml;kningen:&nbsp;</span></p>\n<p>Svar:&nbsp;[[0]]</p>", "marks": 0, "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "gapfill", "variableReplacements": [], "steps": [{"prompt": "<p>The original price of the phone is $&pound;\\var{price}$ and we are told that the price decreases&nbsp;by $\\var{perc}$% every month.</p>\n<p></p>", "marks": 0, "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "information", "variableReplacements": [], "scripts": {}, "variableReplacementStrategy": "originalfirst"}, {"correctAnswerFraction": false, "marks": "0.5", "showFeedbackIcon": true, "prompt": "<p>What is the decimal multiplier for the decrease in the smartphones each month?</p>", "correctAnswerStyle": "plain", "maxValue": "1-{perc}/100", "scripts": {}, "type": "numberentry", "variableReplacements": [], "minValue": "1-{perc}/100", "mustBeReducedPC": 0, "showCorrectAnswer": true, "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacementStrategy": "originalfirst"}, {"marks": "0.5", "allowFractions": false, "precision": "2", "correctAnswerStyle": "plain", "maxValue": "{price}*(1-{perc}/100)", "precisionMessage": "<p>Round your answer to $2$ decimal places.</p>", "scripts": {}, "variableReplacements": [], "precisionType": "dp", "mustBeReduced": false, "correctAnswerFraction": false, "showFeedbackIcon": true, "prompt": "<p>Multiply the original&nbsp;price by the decimal multiplier to obtain the price after 1 month.</p>", "type": "numberentry", "showPrecisionHint": true, "minValue": "{price}*(1-{perc}/100)", "mustBeReducedPC": 0, "showCorrectAnswer": true, "strictPrecision": false, "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"]}, {"marks": "0.5", "allowFractions": false, "precision": "2", "correctAnswerStyle": "plain", "maxValue": "{price}*(1-{perc}/100)^2", "precisionMessage": "<p>Round your answer to $2$ decimal places.</p>", "scripts": {}, "variableReplacements": [], "precisionType": "dp", "mustBeReduced": false, "correctAnswerFraction": false, "showFeedbackIcon": true, "prompt": "<p>Multiply your answer above&nbsp;by the decimal multiplier to obtain the price after 2 months.&nbsp;</p>\n<p>Note that this is the same as multiplying the original price by $d^2$, where $d$ is the decimal multiplier.</p>", "type": "numberentry", "showPrecisionHint": true, "minValue": "{price}*(1-{perc}/100)^2", "mustBeReducedPC": 0, "showCorrectAnswer": true, "strictPrecision": false, "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"]}], "gaps": [{"correctAnswerFraction": false, "marks": "2", "allowFractions": false, "precision": "1", "type": "numberentry", "correctAnswerStyle": "plain", "maxValue": "precround(price*((100-perc)/100)^5, 2)", "precisionMessage": "<p>Avrundning til&nbsp;$1$ desimal.</p>", "scripts": {}, "precisionPartialCredit": 0, "showPrecisionHint": true, "variableReplacements": [], "minValue": "precround(price*((100-perc)/100)^5, 2)", "mustBeReducedPC": 0, "showCorrectAnswer": true, "strictPrecision": false, "showFeedbackIcon": true, "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacementStrategy": "originalfirst"}], "scripts": {}, "stepsPenalty": 0, "variableReplacementStrategy": "originalfirst"}], "tags": [], "preamble": {"css": "", "js": ""}, "rulesets": {}, "advice": "<h4>a)</h4>\n<p>We&nbsp;can use the multiplier method to calculate the new price. If the price decreases by {perc}%, this its value is&nbsp;{100-perc}% of the original value after 1 month. The decimal multiplier for {100-perc}% is</p>\n<p>\\[\\frac{\\var{100-perc}}{100} = \\var{(100-perc)/100} \\text{.}\\]</p>\n<p>Each month our smartphone's value can be found by multiplying the previous month's value by the decimal multiplier. For example, after the first month, the value&nbsp;is</p>\n<p>\\[&nbsp;\\var{(100-perc)/100} \\times\\mathrm{&pound;}\\var{price} = \\mathrm{&pound;}\\var{dpformat(price*(100-perc)/100,2)}\\text{.} \\]</p>\n<p>To calculate the price after 5 months, we multiply the original price of the smartphone by our multiplier&nbsp;5 times:</p>\n<p>\\[ \\begin{align}&nbsp;\\text{Final worth} &amp;=&nbsp;\\var{price} \\times \\var{(100-perc)/100}&nbsp;\\times \\var{(100-perc)/100}&nbsp;\\times \\var{(100-perc)/100}&nbsp;\\times \\var{(100-perc)/100}&nbsp;\\times \\var{(100-perc)/100} \\\\&amp;= &nbsp;\\var{price} \\times \\var{(100-perc)/100}^{5} \\\\&amp;= &pound;\\var{precround(price*((100-perc)/100)^5, 2)} {.}&nbsp;\\end{align}\\]</p>\n<h4>b)</h4>\n<p>From part <strong>a)</strong>, the value after 5 months is &nbsp;&pound;$\\var{precround(price*((100-perc)/100)^5, 2)}$.&nbsp;Continuing to multiply the price by the decimal multiplier,</p>\n<p><span data-jme-visible=\"n&gt;5\">\\[&pound;\\var{precround(price*((100-perc)/100)^5, 2)} \\times \\var{(100-perc)/100} = &pound;\\var{precround(precround(price*((100-perc)/100)^5, 2)*(100-perc)/100, 2)}\\]</span></p>\n<p><span data-jme-visible=\"n&gt;6\">\\[&pound;\\var{precround(price*((100-perc)/100)^5, 2)} \\times \\var{(100-perc)/100}^2 = &pound;\\var{precround(precround(price*((100-perc)/100)^6, 2)*(100-perc)/100, 2)}\\]</span></p>\n<p><span data-jme-visible=\"n&gt;7\">\\[&pound;\\var{precround(price*((100-perc)/100)^5, 2)} \\times \\var{(100-perc)/100}^3 = &pound;\\var{precround(precround(price*((100-perc)/100)^7, 2)*(100-perc)/100, 2)}\\]</span></p>\n<p><span data-jme-visible=\"n&gt;8\">\\[&pound;\\var{precround(price*((100-perc)/100)^5, 2)} \\times \\var{(100-perc)/100}^4 = &pound;\\var{precround(precround(price*((100-perc)/100)^8, 2)*(100-perc)/100, 2)}\\]</span></p>\n<p></p>\n<p>The smartphone's value&nbsp;will be below $&pound;\\var{threshold}$ after&nbsp;<strong>{n-5}</strong> more&nbsp;month<span data-jme-visible=\"n&gt;6\">s</span> ({n} months in total since&nbsp;its release).</p>", "variable_groups": [{"name": "Part a)", "variables": ["price", "perc"]}, {"name": "Part b)", "variables": ["threshold", "pricee1", "pricee2", "pricee3", "testn", "test", "price2", "n", "person"]}], "variables": {"pricee2": {"name": "pricee2", "description": "", "definition": "precround(price*((100 - perc)/100)^(testn-1),2)", "templateType": "anything", "group": "Part b)"}, "test": {"name": "test", "description": "<p>Calculated value of price2 to ensure we mention rounding&nbsp;errors&nbsp;in advice only when needed.</p>", "definition": "precround(precround(price*((100-perc)/100)^5, 2)*((100-perc)/100)^(n-5), 2)", "templateType": "anything", "group": "Part b)"}, "price": {"name": "price", "description": "<p>The original price.</p>", "definition": "random(6000..8000 #100) ", "templateType": "anything", "group": "Part a)"}, "pricee3": {"name": "pricee3", "description": "", "definition": "precround(price*((100 - perc)/100)^(testn-2),2)", "templateType": "anything", "group": "Part b)"}, "testn": {"name": "testn", "description": "<p>Number of months in total.</p>", "definition": "random(6..9)", "templateType": "anything", "group": "Part b)"}, "pricee1": {"name": "pricee1", "description": "<p>The resulting price after the&nbsp;total of testn months.</p>", "definition": "precround(price*((100 - perc)/100)^(testn),2)", "templateType": "anything", "group": "Part b)"}, "n": {"name": "n", "description": "", "definition": "if(pricee2 < threshold, testn-1, testn)", "templateType": "anything", "group": "Part b)"}, "perc": {"name": "perc", "description": "<p>Percentage decrease per month.</p>", "definition": "random(2..4 #0.5)", "templateType": "anything", "group": "Part a)"}, "threshold": {"name": "threshold", "description": "", "definition": "siground(pricee1+5,2)", "templateType": "anything", "group": "Part b)"}, "person": {"name": "person", "description": "", "definition": "random_person()", "templateType": "anything", "group": "Part b)"}, "price2": {"name": "price2", "description": "", "definition": "if(pricee2 < threshold, pricee2, pricee1)", "templateType": "anything", "group": "Part b)"}}, "functions": {}, "statement": "<p>En smartphones verdi minsker hver m&aring;ned med $\\var{perc}$%. N&aring;r den lanseres koster den $\\var{price}$kr.</p>", "extensions": ["random_person"], "ungrouped_variables": [], "variablesTest": {"condition": "", "maxRuns": "1000"}, "type": "question", "contributors": [{"name": "Ida Landg\u00e4rds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2336/"}]}]}], "contributors": [{"name": "Ida Landg\u00e4rds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2336/"}]}