// Numbas version: finer_feedback_settings {"name": "Lineaire recursievergelijkingen met orde 1 (oplossing in breukvorm)", "extensions": ["random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Lineaire recursievergelijkingen met orde 1 (oplossing in breukvorm)", "tags": [], "metadata": {"description": "Stel een differentievergelijking/recursievergelijking op en los op. Gebruik steeds breuken en geen decimalen.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Bij deze oefening noteer je getallen steeds in breukvorm (niet als decimalen), tenzij het om een geheel getal gaat!

", "advice": "

a) Uit de gegevens dat het dagelijkse afbraakpercentage \$\\var{dpct}\$ % bedraagt, en dat er wegens de inname van 1 ml medicament $\\var{s}$ mg {chem} per dag wordt toegevoegd, volgt
\\[ y_{t+1} = y_t - \\var{d} \\cdot y_t + \\var{s} = \\var{1-d} \\cdot y_t + \\var{s} \\]
of in breukvorm
\\[ y_{t+1} = y_t - \\simplify[all,fractionNumbers]{{dpct}/100} \\cdot y_t + \\var{s} = \\simplify[all,fractionNumbers]{{100-dpct}/100} \\cdot y_t + \\var{s} \\]

De beginvoorwaarde is \$ y_0=\\var{b} \$.

\\[\\]

b) De algemene oplossing van een eerste orde recursievergelijking wordt gevonden als som van de algemene oplossing van de geassocieerde homogene recursievergelijking en een particuliere oplossing van de oorspronkelijke recursievergelijking.

De geassocieerde homogene recursievergelijking \$ y_{t+1} = \\simplify[all,fractionNumbers]{{100-dpct}/100} \\cdot y_t \$ heeft als oplossing
\\[ y_t^{H} = C \\cdot \\left( \\simplify[all,fractionNumbers]{{100-dpct}/100} \\right)^t ,\\]
met \$ C \$ een reëel getal.

Om een particuliere oplossing te zoeken van de oorspronkelijke differentievergelijking, imiteren we de rechterhandzijde van
\\[ y_{t+1} - \\simplify[all,fractionNumbers]{{100-dpct}/100} \\cdot y_t = \\var{s} .\\]
Stel daarom \$ y_t = \\alpha\$ met \$ \\alpha \$ een reëel getal, dan is \$ y_{t+1} = \\alpha\$ zodat
\\[ \\alpha - \\simplify[all,fractionNumbers]{{100-dpct}/100} \\cdot \\alpha = \\var{s} \\]
leidt tot
\\[ \\alpha = \\simplify[all,fractionNumbers]{{100*s}/{dpct}} .\\]

Dit geeft als algemene oplossing \\[ y_t = C \\cdot \\left( \\simplify[all,fractionNumbers]{{100-dpct}/100} \\right)^t + \\simplify[all,fractionNumbers]{{100*s}/{dpct}} .\\]

Omdat \$ y_0 = \\var{b} \$ kan je \$ C \$ oplossen uit \\[ \\var{b}= C + \\simplify[all,fractionNumbers]{{100*s}/{dpct}} ,\\] d.w.z.
\\[ C = \\simplify[all,fractionNumbers]{{b-100*s/{dpct}}} .\\]

De uiteindelijke oplossing van de recursievergelijking met beginvoorwaarde is dan
\\[ y_t = \\simplify[all,fractionNumbers]{{b-100*s/{dpct}}} \\cdot \\left( \\simplify[all,fractionNumbers]{{100-dpct}/100} \\right)^t + \\simplify[all,fractionNumbers]{{100*s}/{dpct}} .\\]

\\[\\]

c) De lange termijn concentratie (in mg) van {chem} in het bloed wordt gevonden als limietwaarde voor \$t\$ gaande naar \$ +\\infty \$ van bovenstaande oplossing \$ y_t \$:
\\[ \\simplify[all,fractionNumbers]{{100*s}/{dpct}} .\\]

\\[\\]

d) Stel dat {person['name']} dagelijks \$ x \$ ml medicatie neemt, wat wegens de lineariteitsaanname leidt tot een dagelijkse vermeerdering van de concentratie {chem} in {if(person['gender']='female','haar','zijn')} bloed met \$ \\var{s} \\cdot x \$ mg.
De nieuwe differentievergelijking
\\[ y_{t+1} = \\simplify[all,fractionNumbers]{{100-dpct}/100} \\cdot y_t + \\var{s} \\cdot x \\]
heeft als oplossing
\\[ y_t = C \\cdot \\left( \\simplify[all,fractionNumbers]{{100-dpct}/100} \\right)^t + \\simplify[all,fractionNumbers]{{100*s}/{dpct}} \\cdot x \\]
met lange termijn evenwichtsconcentratie
\\[ \\simplify[all,fractionNumbers]{{100*s}/{dpct}} \\cdot x .\\]

Om op lange termijn \$ \\var{lt} \$ mg {chem} in het bloed te bekomen, geldt dan
\\[ \\simplify[all,fractionNumbers]{{100*s}/{dpct}} \\cdot x = \\var{lt} ,\\]
of met andere woorden
\\[ x = \\simplify[all,fractionNumbers]{{lt*dpct}/{100*s}} ,\\]
zodat je (benaderend) \$ \\var{opld} \$ ml medicatie nodig hebt.

\\[\\]

e) De differentievergelijking
\\[ y_{t+1} = \\simplify[all,fractionNumbers]{{100-dpct}/100} \\cdot y_t + \\simplify[all,fractionNumbers]{{lt*dpct}/{100}} \\]
heeft nu als oplossing
\\[ y_t = \\var{b - lt} \\cdot \\left( \\simplify[all,fractionNumbers]{{100-dpct}/100} \\right)^t + \\var{lt} .\\]

Om voor het eerst minder dan {Gpct}% van de vooropgestelde limiet \$ \\var{lt} \$ mg {chem} in het bloed te bekomen, moet
\\[ \\var{b - lt} \\cdot \\left( \\simplify[all,fractionNumbers]{{100-dpct}/100} \\right)^t + \\var{lt} < \\simplify[all,fractionNumbers]{{Gpct*lt}/{100}} \\]
d.w.z.
\\[ \\var{b - lt} \\cdot \\left( \\simplify[all,fractionNumbers]{{100-dpct}/100} \\right)^t < \\simplify[all,fractionNumbers]{{(Gpct-100)*lt}/{100}} \\]
of equivalent
\\[ \\left( \\simplify[all,fractionNumbers]{{100-dpct}/100} \\right)^t < \\simplify[all,fractionNumbers]{{(Gpct-100)*lt}/{100*({b-lt})}} .\\]

Toepassing van de (natuurlijke) logaritme op de linker- en rechterhandzijde behoudt de ongelijkheid (omdat $\\ln$ een stijgende functie is):
\\[   t \\cdot \\ln \\left( \\simplify[all,fractionNumbers]{{100-dpct}/100} \\right)   < \\ln \\left( \\simplify[all,fractionNumbers]{{(Gpct-100)*lt}/{100*({b-lt})}}\\right) ,\\]
i.e.
\\[   t \\cdot (\\var{Ne}) < \\var{Te} ,\\]
wat gelijkwaardig is met
\\[   t > \\var{Be} \\]
(de ongelijkheid werd omgekeerd omdat je deelt door een strikt negatief getal).

Afronding naar boven levert een tijd op van \$ \\var{ceil(Be)} \$ dagen om voor het eerst minder dan {Gpct}% van de vooropgestelde limiet \$ \\var{lt} \$ mg {chem} in het bloed te bekomen.

\\[\\]

f) Veronderstel dat het lichaam van {person['name']} dagelijks $x$% afbreekt van {chem} en dat {person['name']} dagelijks 1 ml medicatie gebruikt, met $ 0 < x < 100$. Dan heeft de bijhorende recursievergelijking
\\[ y_{t+1} = y_t - {\\frac{x} {100}} \\cdot y_t + \\var{s} ,\\]
als oplossing
\\[ y_t = \\left( {\\var{b}}-{\\frac {\\var{100*s}} {x}} \\right)\\cdot \\left( {1 - {\\frac{x} {100}}} \\right)^t + {\\frac{\\var{100*s}} {x}} ,\\]
met als lange termijn concentratie
\\[ {\\frac{\\var{100*s}} {x}} .\\]
Om dus op lange termijn {lt1} mg {chem} in het bloed te bekomen, moet
\\[ x = \\simplify[all,fractionNumbers]{{100*s}/{lt1}} .\\]
Bijgevolg dient {person['name']} dagelijks (benaderend) \$ \\var{oplf} \$ % {chem} af te breken.

", "rulesets": {}, "extensions": ["random_person"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"s": {"name": "s", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "

stijging mg

", "templateType": "anything", "can_override": false}, "d1pct": {"name": "d1pct", "group": "Ungrouped variables", "definition": "100*d1", "description": "", "templateType": "anything", "can_override": false}, "lt1": {"name": "lt1", "group": "Ungrouped variables", "definition": "random(6..10)", "description": "", "templateType": "anything", "can_override": false}, "verschil": {"name": "verschil", "group": "Ungrouped variables", "definition": "random(1..7)", "description": "

b-lt=verschil

", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "dpct/100", "description": "", "templateType": "anything", "can_override": false}, "Te": {"name": "Te", "group": "Ungrouped variables", "definition": "ln((Gpct-100)*lt/(100*(b-lt)))", "description": "", "templateType": "anything", "can_override": false}, "chem": {"name": "chem", "group": "Ungrouped variables", "definition": "random([\"Thiotamoline\",\"Thiotemoline\",\"Thiotomoline\",\"Thiotumoline\"])", "description": "", "templateType": "anything", "can_override": false}, "Ne": {"name": "Ne", "group": "Ungrouped variables", "definition": "ln(1-d)", "description": "", "templateType": "anything", "can_override": false}, "dpct": {"name": "dpct", "group": "Ungrouped variables", "definition": "random(2..20)", "description": "

afbraakpercentage

", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "", "templateType": "anything", "can_override": false}, "person": {"name": "person", "group": "Ungrouped variables", "definition": "random_person()", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "lt+verschil", "description": "

beginwaarde

", "templateType": "anything", "can_override": false}, "Gpct": {"name": "Gpct", "group": "Ungrouped variables", "definition": "100+g", "description": "", "templateType": "anything", "can_override": false}, "tgrens": {"name": "tgrens", "group": "Ungrouped variables", "definition": "ceil(ln(g*lt/(100*verschil))/ln(1-d))", "description": "", "templateType": "anything", "can_override": false}, "oplf": {"name": "oplf", "group": "Ungrouped variables", "definition": "decimal(round(100*d1pct)/100)", "description": "", "templateType": "anything", "can_override": false}, "d1": {"name": "d1", "group": "Ungrouped variables", "definition": "s/lt1", "description": "", "templateType": "anything", "can_override": false}, "lt": {"name": "lt", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "

langetermijn

", "templateType": "anything", "can_override": false}, "Be": {"name": "Be", "group": "Ungrouped variables", "definition": "Te/Ne", "description": "", "templateType": "anything", "can_override": false}, "opld": {"name": "opld", "group": "Ungrouped variables", "definition": "decimal(round(100*lt*d/s)/100)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["dpct", "s", "lt", "verschil", "b", "d", "g", "Gpct", "tgrens", "lt1", "d1", "d1pct", "opld", "Te", "Ne", "Be", "chem", "oplf", "person"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "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": "

Opgave

Vanmorgen, bij het begin van de dag, had {person['name']} {b} mg {chem} (een chemische stof) in {if(person['gender']='female','haar','zijn')} bloed.
{if(person['gender']='female','Zij','Hij')} neemt elke dag 1 ml medicatie in, waardoor aan het begin van de volgende dag de hoeveelheid {chem} vermeerdert met {s} mg.
{if(person['gender']='female','Haar','Zijn')} lichaam breekt dagelijks {dpct}% af van de hoeveelheid die in het begin van de dag aanwezig is.
Beschouw de tijd $t$ als een discrete grootheid en noteer met $y_t$ het aantal mg {chem} dat over $t$ dagen aan het begin van de dag in {if(person['gender']='female','haar','zijn')} bloed aanwezig zal zijn.

"}, {"type": "gapfill", "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": "

Stel een recursievergelijking met beginvoorwaarde op voor de rij $y$ in de vorm $y_{t+1} = getal1 \\cdot y_t + getal2$ :

$y_{t+1}$ = [[0]] $\\cdot y_t$ + [[1]] met BVW (beginvoorwaarde) $y_0=$ [[2]]

", "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": "{1-{d}}", "answerSimplification": "all,fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "$n/$n", "partialCredit": 0, "message": "Je mag geen decimalen gebruiken.", "nameToCompare": "", "warningTime": "submission"}, "valuegenerators": []}, {"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": "{s}", "answerSimplification": "all,fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "$n", "partialCredit": 0, "message": "", "nameToCompare": "", "warningTime": "submission"}, "valuegenerators": []}, {"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, "minValue": "b", "maxValue": "b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "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": "

Los deze recursievergelijking uit a) op onder de gedaante $y_t = getal1 \\cdot grondtal^t + getal2$.

$y_t$ = [[0]] $\\cdot$ [[1]] $+$ [[2]]

", "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": "{b-s/d}", "answerSimplification": "all,fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "`! m_anywhere(decimal:$n)", "partialCredit": 0, "message": "Je mag geen decimalen gebruiken.", "nameToCompare": "", "warningTime": "submission"}, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({1-d})^t", "answerSimplification": "all,fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "`! m_anywhere(decimal:$n)", "partialCredit": 0, "message": "Schrijf jouw oplossing als (breuk)^t.", "nameToCompare": "", "warningTime": "submission"}, "valuegenerators": [{"name": "t", "value": ""}]}, {"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": "{s/d}", "answerSimplification": "all,fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "`! m_anywhere(decimal:$n)", "partialCredit": 0, "message": "Je mag geen decimalen gebruiken.", "nameToCompare": "", "warningTime": "submission"}, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "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": "

Hoeveel mg {chem} zal het bloed van {person['name']} in de gegeven omstandigheden op lange termijn bevatten?

[[0]]

Idealiter zou {person['name']} op lange termijn {lt} mg {chem} in {if(person['gender']='female','haar','zijn')} bloed hebben. Hoeveel constante ml medicatie moet {if(person['gender']='female','zij','hij')} daarvoor dan dagelijks verbruiken (in de veronderstelling dat de medicatie op lineaire wijze leidt tot een vermeerdering van de chemische stof {chem} in het bloed)?

[[0]]

", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{lt*d/s}", "answerSimplification": "all,fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "$n/$n`|$n", "partialCredit": 0, "message": "Je mag geen decimalen gebruiken.", "nameToCompare": "", "warningTime": "submission"}, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "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": "

Na hoeveel dagen zal {person['name']}, met de doelstelling uit d), voor het eerst minder dan {Gpct}% van de vooropgestelde limiet in {if(person['gender']='female','haar','zijn')} bloed hebben?

[[0]]

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "tgrens", "maxValue": "tgrens", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "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": "

Veronderstel dat het lichaam van {person['name']} dagelijks geen {dpct}%, maar een ander (constant) percentage afbreekt. Hoe groot is dat percentage als blijkt dat {if(person['gender']='female','zij','hij')} op lange termijn {lt1} mg {chem} in {if(person['gender']='female','haar','zijn')} bloed heeft (in de oorspronkelijke veronderstelling dat {if(person['gender']='female','zij','hij')} dagelijks 1 ml medicatie gebruikt)?

[[0]]

", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{d1pct}", "answerSimplification": "all,fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "$n/$n`|$n", "partialCredit": 0, "message": "Je mag geen decimalen gebruiken.", "nameToCompare": "", "warningTime": "submission"}, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Paul Verheyen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3610/"}, {"name": "Dirk Janssens", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3705/"}], "resources": []}]}], "contributors": [{"name": "Paul Verheyen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3610/"}, {"name": "Dirk Janssens", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3705/"}]}