// Numbas version: exam_results_page_options
{"name": "Mat 2B - UTS - No 7", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Mat 2B - UTS - No 7", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Misal laju transkripsi berubah secara eksponensial terhadap fungsi $e^{\\var{b} t }$ dan mRNA mempunyai laju peluruhan konstan $\\var{k}$. Banyaknya molekul transkrip mRNA, dinotasikan $T$, berubah melalui persamaan diferensial</p>\n<p style=\"text-align: center;\">$\\dfrac{dT}{dt}=e^{\\var{b} t}-\\var{k}T.$</p>", "advice": "", "rulesets": {}, "extensions": [], "variables": {"k": {"name": "k", "group": "Ungrouped variables", "definition": "random(1,2,3,4,5)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(0.1,0.2,0.3,0.4,0.5)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["k", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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>Misalkan $T(0)=\\dfrac{1}{\\simplify{{k}+{b}}}$. Dengan ketelitian $3$ angka di belakang koma, tentukan nilai dari $T\\left( \\dfrac{1}{2} \\right)$.</p>\n<p><em>Petunjuk</em>: Gunakan substitusi $y(t)=e^{\\var{k}t}T(t)$ agar dapat masalah nilai awal tersebut dapat diselesaikan dengan metode separasi variabel</p>", "minValue": "e^(0.5*b)/(k+b)", "maxValue": "e^(0.5*b)/(k+b)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Dengan menggunakan Metode Euler untuk $h=0.25$, akan diperoleh $T_1(0.25) \\approx\\ldots$.</p>", "minValue": "(4-k)/(4*(k+b))+1/4", "maxValue": "(4-k)/(4*(k+b))+1/4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Titik kedua yang diperoleh dari Metode Euler adalah $T_2(0.5) \\approx\\ldots$.</p>", "minValue": "(4-k)/(4*(k+b))+1/4+1/4*e^(0.25*b)-k*(4-k)/(k+b)/16-k/16", "maxValue": "(4-k)/(4*(k+b))+1/4+1/4*e^(0.25*b)-k*(4-k)/(k+b)/16-k/16", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": 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>Tentukan galat mutlak Metode Euler, $|T(0.5)-T_2(0.5)|$.</p>", "minValue": "abs((4-k)/(4*(k+b))+1/4+1/4*e^(0.25*b)-k*(4-k)/(k+b)/16-k/16-(e^(0.5*b)/(k+b)))", "maxValue": "abs((4-k)/(4*(k+b))+1/4+1/4*e^(0.25*b)-k*(4-k)/(k+b)/16-k/16-(e^(0.5*b)/(k+b)))", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}]}]}], "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}]}