// Numbas version: exam_results_page_options
{"name": "Compound interest from graph", "extensions": [], "custom_part_types": [], "resources": [["question-resources/exp1.png", "/srv/numbas/media/question-resources/exp1.png"], ["question-resources/exp2.png", "/srv/numbas/media/question-resources/exp2.png"], ["question-resources/exp3.png", "/srv/numbas/media/question-resources/exp3.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Compound interest from graph", "tags": [], "metadata": {"description": "<p>Shows an exponential graph&nbsp;displaying the value of an investment under compound interest. Students have to identify the type of graph and answer 3 questions about the value of the investment from the graph.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>The following graph shows the value of an investment that is compounded at&nbsp;{rates[idx]} % per annum.&nbsp;</p>\n<p>The x-axis shows the time of investment in years, and the y-axis shows the investment value.</p>\n<p>{image('resources/question-resources/'+images[idx])}</p>", "advice": "<p>This is an exponential graph.</p>\n<p>The initial value of the investment is the value where the graph cuts the $y$-axis. This is the value of the investment when time = 0, at the start of the investment. This is \\${initials[idx]}.</p>\n<p>The investment starts at \\${initials[idx]} so to double it needs to reach \\${2*initials[idx]}.</p>\n<p>We find \\${2*initials[idx]} on the $y$-axis. Then we go across until we meet the graph. Then we go down to the $x$ axis and read off the value there. We need to be careful doing this, because the marker lines on the axis may not be 1 year apart. In this case,&nbsp;the marker lines are {gradations[idx]} apart, and the time for the investment to double is {doubles[idx]} years.</p>\n<p>Observe that {2*investment} = 2 $\\times$ {investment}.</p>\n<p>Because this is an exponential graph, the time taken for the investment to double is constant. Therefore the time taken for an initial investment of \\${investment} to reach \\${2*investment} is {doubles[idx]} years.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"images": {"name": "images", "group": "Ungrouped variables", "definition": "['exp1.png','exp2.png','exp3.png']", "description": "", "templateType": "anything", "can_override": false}, "rates": {"name": "rates", "group": "Ungrouped variables", "definition": "[5,2.5,8]", "description": "", "templateType": "anything", "can_override": false}, "initials": {"name": "initials", "group": "Ungrouped variables", "definition": "[1,20,100]", "description": "", "templateType": "anything", "can_override": false}, "idx": {"name": "idx", "group": "Ungrouped variables", "definition": "random(0..2)", "description": "", "templateType": "anything", "can_override": false}, "doubles": {"name": "doubles", "group": "Ungrouped variables", "definition": "[14,28,9]", "description": "", "templateType": "anything", "can_override": false}, "gradations": {"name": "gradations", "group": "Ungrouped variables", "definition": "['2 years','2 years','1 year']", "description": "", "templateType": "anything", "can_override": false}, "investment": {"name": "investment", "group": "Ungrouped variables", "definition": "random(1..10000)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["images", "rates", "initials", "idx", "doubles", "gradations", "investment"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What type of graph is this?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["exponential", "quadratic", "linear", "inverse"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}, {"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 value of the investment in dollars?</p>", "minValue": "{initials[idx]}", "maxValue": "{initials[idx]}", "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>How many years does it take for the value of the investment to double?</p>", "minValue": "{doubles[idx]}", "maxValue": "{doubles[idx]}", "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>If \\${investment} was invested at this same interest rate, how many years would it take for the value of the investment to reach \\${2*investment}?</p>", "minValue": "{doubles[idx]}", "maxValue": "{doubles[idx]}", "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", "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/"}]}