// Numbas version: finer_feedback_settings
{"name": "The System", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "The System", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>The first order compartment model for pharmacokinetics describes the passage of an ingested compound, such as theophylline, from the stomach into the bloodstream. Over the course of a few hours, the amount in the stomach, $y_1(t)$, and bloodstream, $y_2(t)$, vary from their initial values.</p>\n<p>The compound is absorbed from the stomach into the bloodstream, such that the rate of change of the amount in the stomach is given by the following model:</p>\n<p>$\\frac{dy_1}{dt} = -k_a y_1$</p>\n<p>with initial amount $y_1(0) = c_0$ having units mg (milligrams).</p>", "advice": "", "rulesets": {}, "extensions": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Given the information about the units of $y_1$ and $t$, state the units of $k_a$.</p>", "answer": "per hour|/hour|per hr|hr\\^-1|hour^-1|/hr", "displayAnswer": "", "matchMode": "regex"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The rate of change of the amount in the bloodstream is driven by the absorption from the stomach as well as the clearance of the compound from the bloodstream through the kidneys, with rate parameter $k_c = $. The model is</p>\n<p>$\\frac{dy_2}{dt} = k_a y_1 - k_c y_2$</p>\n<p>What is an appropriate initial condition for the amount of the compound in the bloodstream (in mg)?</p>\n<p></p>", "minValue": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Given the information about the units of $y_1$, $y_2$, $k_a$ and $t$, state the units of $k_c$.</p>", "answer": "per hour|/hour|per hr|hr\\^-1|hour^-1|/hr", "displayAnswer": "", "matchMode": "regex"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Belinda Spratt", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7204/"}]}]}], "contributors": [{"name": "Belinda Spratt", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7204/"}]}