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Now that you have solved the differential equations, we will visualise the solution in R.

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Modify the following code to create a function that calculates the amount of Theophylline in the blood at time $t$.

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calculate_blood_amount <- function(t, parms){
 
  c_0 <- parms[1]
  k_a <- parms[2]
  k_c <- parms[3]
 
  return([[0]])
 
}

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Modify the following code to plot the amount of Theophylline in the bloodstream during the first 24 hours after ingestion.

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Here, use the values $k_a = ${k_a}, $k_c = ${k_c} and $c_0 = ${c_0}.

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parms <- c([[0]],[[1]],[[2]])

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ggplot(data = data.frame(x = [[3]]), aes([[4]]))+

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stat_function(fun = [[5]], args = [[6]])+

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ggtitle(\"Amount of Theophylline in the bloodstream\")+

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theme_bw()

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Tip: Don't include spaces in your answers.

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Create a data frame containing a sequence of times from 0 to 24 hours in fifteen-minute increments. Create two columns, Stomach and Bloodstream containing, respectively, the amounts of the compound in the stomach and bloodstream. Fill in the following table to show the concentrations in both the stomach and bloodstream during the first two hours (in fifteen-minute increments).

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Remember, your values are $k_a = ${k_a}, $k_c = ${k_c} and $c_0 = ${c_0}.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Time (minutes)Stomach (mg)Bloodstream (mg)
0[[0]][[9]]
15[[1]][[10]]
30[[2]][[11]]
45[[3]][[12]]
60[[4]][[13]]
75[[5]][[14]]
90[[6]][[15]]
105[[7]][[16]]
120[[8]][[17]]
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Tip: Be sure to enter the solutions correct to two decimal places.

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