// Numbas version: exam_results_page_options
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From that point, we draw a line vertically to find a point on the graph. From the point on the graph, we need to draw a horizontal line, and then estimate the value of $p$.&nbsp;</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/wnracghs',&nbsp;defsad)}</p>\n<p>Here, a good estimate could be $p=\\var{ans_a_rounded} $.</p>\n<p>b) We first need to estimate the point where the $\\var{p_1*100}$% would lay on would lie on the p-axis. That is $ \\frac{\\var{p_1*100}}{100}=\\var{p_1}$. From here, we draw a line horizontally to find a point on the graph. From the point on the graph, we draw a vertical line, and then estimate the value of $t$.&nbsp;</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/wnracghs', defsad1)}</p>\n<p>Here, a good estimate could be $\\var{ans_t}$ seconds.</p>\n<p>c) At 7 seconds, the proportion of sodium carbonate which has dessolved is $p=1$ or, if transformed to a percentage, $100$%. That means all the sodium carbonate will have dissolved completely at $t=7$ seconds and the quadratic graph&nbsp; cannot describe the situation beyond the 7 seconds.</p>", "rulesets": {}, "extensions": ["geogebra"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Problem posing variables", "definition": "random (1 ..5 )", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Problem posing variables", "definition": "Random(50..90)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Problem posing variables", "definition": "random(100..400 #10)", "description": "", "templateType": "anything", "can_override": false}, "p_1": {"name": "p_1", "group": "Problem posing variables", "definition": "random(0 .. 1 # 0.1 except [ 0 , 1 ] )", "description": "", "templateType": "anything", "can_override": false}, "t_1": {"name": 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"showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Use the graph to estimate the proportion of sodium carbonate which has dissolved after $\\var{t_1}$ seconds.</p>\n<p><em>$p=$ [[0]]</em></p>\n<p><em>Give your answer as a decimal, if needed, rounded to 2 decimal places.</em></p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ans_a}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": "0.025", "failureRate": 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You can choose only <span style=\"text-decoration: underline;\">one</span> of the answers.</p>\n<p>[[0]]</p>", "gaps": [{"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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["After $\\var{tmax}$ seconds, the volume of sodium carbonate is removed from the beaker.", "After $\\var{tmax}$ seconds, the sodium carbonate will continue dissolving at a different rate.", "After $\\var{tmax}$ seconds, the sodium carbonate will have dissolved completely.", "After $\\var{tmax}$ seconds, the proportion will be negative, $p\\leq 0$."], "matrix": [0, 0, "1", 0], "distractors": ["", "", "", ""]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}, {"name": "Evi Papadaki", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18113/"}]}]}], "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}, {"name": "Evi Papadaki", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18113/"}]}