Effectiveness of a drug On a scale from 0 to 1, the effectiveness E of a pain-killing drug t hours after entering the bloodstream is displayed in the accompanying figure. 1.0 0.8 0.6 0.4 0.2 3 4 5 At what times does the effectiveness appear to be increasing? a. What is true about the derivative at those times? b. At what time would you estimate that the drug reaches its maximum effectiveness? What is true about the derivative at that time? What is true about the derivative as time increases in the 1 hour before your estimated time?

Many patients get concerned when a test involves injection of a radioactive material. For example for scanning a gallbladder, a few drops of Technetium-99m isotope is used. However, it takes about 24 hours for the radiation levels to reach what we are exposed to in day-to-day activities. Below is given the relative intensity of radiation as a function of time. t(hrs) 0 1 3 5 7 9 R 1.000 0.891 0.708 0.562 0.447 0.355 The relative intensity is related to time by the equation R = A e^(Bt). Find the constant A by the least square method. (correct to 4 decimal places) -0.05

(a) Fill in the table. Hint: Some of the values are listed on the vertical axis. (Type an integer or decimal rounded to one decimal place as needed.) Amount Q, 12.87 Time, t, (hours) (mg) Number 2 12.8 4 6.4 3.2 8 Number 6.4- 10 Number 12 Number 3.2- 2 4 8. 10 12 14 16 (b) Report the half-life. Use the pull-down menu to report the units. The half-life is Number Click for List (c) Write a formula which gives Q as a function of t. The parameters in the formula should not contain rounded values. Include 0.5 in your formula. Q = OEP (Your answer involves 0.5, real numbers, and a lower case t.) TIP: If desired, click on the Plot icon () next to the answer box to graph your response. (Although your answer may match the graph, it will be counted incorrect if it is not in the form requested.) (d) Estimate the length of time until the amount of the drug in the patient's bloodstream is 0.2 mg. After Number hours, the amount of drug in the bloodstream is 0.2 mg. (Type an integer or decimal…