Caffeine Elimination Rate

 Time (hrs.) Caffeine (mg) 0 48.00 1 38.11 2 30.26 3 24.03 4 19.08 5 15.15 6 12.03 7 9.55 8 7.58 9 6.02 10 4.78 11 3.80 12 3.01 13 2.39 14 1.90 15 1.51 16 1.20 17 0.95 18 0.76 19 0.60 

The human body processes different drugs in different ways. Most of you have probably observed that a drunken person does not stay drunk forever. Sooner or later, the blood alcohol concentration (BAC) returns to zero. Alcohol is a rather unusual chemical in terms of how the body processes it. To understand it better, let's compare it with the caffeine in an average soft drink.

Assume that you quickly drink a 12 oz. soft drink containing about 48 mg of caffeine. If the amount of caffeine in your body were monitored over the next 19 hours, the result would be similar to the data in this table.

1. Make a scatter plot in Excel of the data (time, caffeine) from the table.

2. Examine the scatter plot and the table. How would you best describe the trend?

3. Determine the best trendline equation for the graph. Write it here, in standard form.

4. The standard form of the equation for this graph is . Explain the meaning of the constant a in this equation.

5. Determine the decay rate, r, of this function. Write it here. Explain the meaning of this rate in the context of the problem.

6. What does half-life mean? What is the half-life of caffeine in this particular scenario?

7. When will your body have eliminated all the caffeine?

Please, show all your works. I need specific answers. Thanks.