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Now that you have solved the differential equations, we will visualise the solution in R.
", "advice": "", "rulesets": {}, "extensions": [], "variables": {"k_c": {"name": "k_c", "group": "Ungrouped variables", "definition": "random(0.3 .. 2.7#0.01)", "description": "", "templateType": "randrange"}, "k_a": {"name": "k_a", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.25#0.01)", "description": "", "templateType": "randrange"}, "c_0": {"name": "c_0", "group": "Ungrouped variables", "definition": "random(150 .. 530#1)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["k_c", "k_a", "c_0"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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": "Modify the following code to create a function that calculates the amount of Theophylline in the blood at time $t$.
\n\ncalculate_blood_amount <- function(t, parms){
c_0 <- parms[1]
k_a <- parms[2]
k_c <- parms[3]
return([[0]])
}
Modify the following code to plot the amount of Theophylline in the bloodstream during the first 24 hours after ingestion.
\n\nHere, use the values $k_a = ${k_a}, $k_c = ${k_c} and $c_0 = ${c_0}.
\n\nparms <- c([[0]],[[1]],[[2]])
\n\nggplot(data = data.frame(x = [[3]]), aes([[4]]))+
\nstat_function(fun = [[5]], args = [[6]])+
\nggtitle(\"Amount of Theophylline in the bloodstream\")+
\ntheme_bw()
\n\nTip: Don't include spaces in your answers.
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\nRemember, your values are $k_a = ${k_a}, $k_c = ${k_c} and $c_0 = ${c_0}.
\nTime (minutes) | \nStomach (mg) | \nBloodstream (mg) | \n
0 | \n[[0]] | \n[[9]] | \n
15 | \n[[1]] | \n[[10]] | \n
30 | \n[[2]] | \n[[11]] | \n
45 | \n[[3]] | \n[[12]] | \n
60 | \n[[4]] | \n[[13]] | \n
75 | \n[[5]] | \n[[14]] | \n
90 | \n[[6]] | \n[[15]] | \n
105 | \n[[7]] | \n[[16]] | \n
120 | \n[[8]] | \n[[17]] | \n
Tip: Be sure to enter the solutions correct to two decimal places.
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