Rate of Change Writing Assignment

Suppose that the concentration c of a drug in the blood t hours after it is taken is given by

, where t is in hours and c is in ppm (parts per million).

1) Enter this function on your calculator, using the window X:[0,7] and Y:[-1,5].

2) Using your graph or the function directly, find the concentration at a) 30 minutes, and b) 6 hours after the drug is taken. Don’t forget units.

3) At about t = 1.12 hours, the drug concentration is at a maximum. What is the maximum drug concentration?

4) By examining the graph, explain what is happening to the concentration at….

a) t = 30 minutes, b) t = 1.12 hours, and c) t = 6 hours after the drug is taken.

Write a sentence for each based on a visual interpretation of the graph,

not based on numerical values.

5) Now find using the quotient rule. Simplify the numerator appropriately.

6) Find the rate of change of concentration at the three different times referred to in #4 above. In other words, compute , , and . Round your answers to the nearest tenth. Include units on your answers.

7) Using only values you have calculated thus far (i.e. in #2 and #6), compute an estimate for the concentration at t = 7 hours. Include units.

8) For each of t = .5, t = 1.12 and t = 6 hours, make connections between the derivative values from #6 and your graph observations in #4. Use complete sentences. Also write a short summary that tells the overall story of the drug concentration over the first 6 hours, and in a general way ties together the c(t) graph with derivative values.