# Math 1010 drug filtering lab

Math 1010        Drug Filtering Lab

The purpose of this lab is to come up with a continuous model for exponential decay.

Dot assumes that her kidneys can filter out 25% of a drug in her blood every 4 hours.   She knows that she will need to take a drug test for an interview in a couple of days.  She plans on taking one 1000-milligram dose of the drug to help manage her pain.

1.)  Fill in the table showing the amount of the drug in your blood as a function of time and round each value to the nearest milligram. The first two data points are already completed.

 TIME SINCE TAKING THE DRUG (HR) AMOUNT OF DRUG IN HER BLOOD (MG) 0 1000 4 750 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68

What might a model for this data look like?

2.)  Use a graphing utility to make a plot of the above data.  Label axes appropriately.

3.)  Based on your graph, what can you say about the data?  For example, is there a pattern? Is there constant slope?

4.)  How many milligrams of the drug are in Dot’s blood after 2 days?

5.)  How many milligrams of the drug are in Dot’s blood after 5 days?

6.)  How many milligrams of the drug are in Dot’s blood 30 hours after she took the drug?  Explain your reasoning.

7.)  A blood test is able to detect the presence of this drug if there is at least 0.1 mg in a person’s blood.How many days will it take before the test will come back negative? Explain your answer.

8.)  Will the drug ever be completely removed from her system? Explain your reasoning. What complications might arise from having excess amounts in her system?

9.)  Since there is a constant rate of decay, a continuous exponential decay model can be used to determine how much drug is in her system at any time.

Exponential Decay Model

Where A(t) is amount of drug in blood at time t in hours,

A0 is the initial amount of drug, and

k is the rate of decay (it will be a negative number)

You will have to find the actual value of k that works for this model.  Write down the exponential decay model for the amount of drug in Dot’s blood as a function of time:

Now use that model to fill in the following table:

 TIME SINCE TAKING THE DRUG (HR) AMOUNT OF DRUG IN HER BLOOD (MG) 0 1000 4 750 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68

10.)               Interpret the parameters of this exponential model in terms of the context of the problem.

11.)               Compare your values with the estimated values in the model.  How close were they?  Why might they be different?

12.)               Use a graphing utility to graph the original data along with a graph of the model on the same set of axes.

13.)               Were you expecting a horizontal asymptote?  What might that mean in the context of the problem?

14.)               Using your model, how much drug is in her system 17 hours after taking the drug?

15.)               Using your model, how long will it take for exactly one-half of the drug to remain in her system?

16.)               Using this model, how long will it take for 0.1 mg of the drug to remain in her system?

17.)               Do you think the continuous decay model is more accurate for predicting the amount of drug in her blood?  Why?  Or why not?

18.)               What other factors should be considered in coming up with a more realistic model?

19.)               Reflective writing: Did this project change the way you think about how math can be applied to the real world? Write one paragraph stating what ideas changed and why. If this project did not change the way you think, write how this project gave further evidence to support your existing opinion aboutapplying math. Be specific.

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