Math 1 Exponential Functions The Marvel of Medicine

Math 1 Exponential Functions: The Marvel of Medicine Irina Keith adapted by WCPS

The Marvel of Medicine Task › Mathematical Goals › Apply exponential functions to real-life situations. › Analyze exponential functions in context. › Essential Questions › How do we interpret exponential functions in context? › How do we use exponential functions to represent real-life situations? › › * The task is adapted from the Dana Center.

The Marvel of Medicine › Part I. A doctor prescribes 400 milligrams of medicine to treat an infection. Each hour following the initial dose, 85% of the concentration remains in the body from the preceding hour. › 1). Represent the amount of medicine remaining after each hour in the forms of a table and a graph. Discuss the domain and range of the situation. Hour 0 1 2 3 4 5 Process Number of Milligrams Remaining in the Body

The Marvel of Medicine Number of Hours Process 0 400 1 400 (0. 85) 400(0. 85)1 400 (0. 85) 400(0. 85)2 400 (0. 85)(0. 85) 400(0. 85)3 400 (0. 85)(0. 85) 400(0. 85)4 400 (0. 85)(0. 85) 400(0. 85)5 2 3 4 5 Solutions Repeated multiplication by 0. 85 was used to complete the table. Number of Milligrams Remaining in the Body 400 340 289 245. 65 208. 8 177. 48

Graph Amount of Medicine Left in Body (mg) Amount of Medicine Left in Body 450 400 340 350 289 300 245. 65 250 208. 8 200 177. 48 150. 86 150 128. 23 108 92. 65 100 78. 75 66. 94 56. 9 50 0 0 1 2 3 4 5 6 Hour 7 8 9 10 11 12

The Marvel of Medicine › 2). Using symbols and words, describe the functional relationship in this situation. › 3). Suppose that the level of medicine in the patient’s body must maintain a level greater than 100 milligrams. How often does the patient need to take the medicine? › 4). When does the amount of medicine still in the body reach 60 milligrams? Explain how you know.

The Marvel of Medicine: What If? › Part II. What if? › 1). If the rule had been y = 500(0. 85)x instead of y = 400(0. 85)x, how would this situation be different from the given situation? › 2). What would the equation be if the concentration of medicine decreased by 30% each hour? › 3). If the patient took a second 400 -milligram dose at the end of the twelfth hour, how much medicine would the patient have in his system at the end of the fifteenth hour?