Week 1: Section 1.2-1.3 Recitation 2 Math 106 Spring 2016 sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m Problem 1. Fold a piece of paper in half, then in half again, then in half again. How many times do you believe you would be able to fold a single piece of paper in half ? Test your hypothesis. Problem 2. Standard printer paper has a thickness of 0.1mm. Write an equation for a function that should approximate the thickness of a sheet of paper after n folds. Th Problem 3. Explain why it would be unreasonable to claim you have folded a singe piece of paper 20 times. https://www.coursehero.com/file/18887129/Recitation-2-Handout/ 2 Week 1: Section 1.2-1.3 Recitation 2 Math 106 Spring 2016 Problem 4. As your altitude increases the air density decreases. In airplanes, the decrease in air density decreases the performance of the engine leading to longer take-o ground rolls. If we assume a constant temperature of about 70 F then the ground roll distance for a fully loaded Cessna 172 is given below. Elevation (ft) Ground roll (ft) 0 585 1000 640 2000 700 3000 770 4000 845 5000 930 6000 1025 7000 1130 8000 1245 100 1000 sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m On the following set of axis sketch the graph of a function that approximates the ground roll for a fully loaded Cessna 172 at an elevation of x feet. Problem 5. Based on your picture what type of function do you think describes the ground roll for a fully loaded Cessna 172 at an elevation of x feet. Th Problem 6. Use the data and create a formula for the function that approximates the ground roll for a fully loaded Cessna 172 at an elevation of x feet. https://www.coursehero.com/file/18887129/Recitation-2-Handout/ 3 Week 1: Section 1.2-1.3 Recitation 2 Math 106 Spring 2016 Problem 7. Many pilots are trained to estimate the takeo ground roll by a method called linear interpolation. Instead of explaining what linear interpolation is we provide an example. Your task is to break down the example. Understand what is going on and then critique the example. Richard is planning to depart from the Sidney Municipal Airport in Sidney NE. The airport has an elevation of 4314 feet and the temperature is currently 70 F. In order to calculate how much runway he needs to depart Richard uses linear interpolation. Specifically, Richard performs the following set of calculations. 845 314 + 845 = 871.69 4000 sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m 930 5000 Richard therefore concludes that he will only need 872 feet for takeo. Th Is this a reasonable conclusion? https://www.coursehero.com/file/18887129/Recitation-2-Handout/ 4 Week 1: Section 1.2-1.3 Recitation 2 Math 106 Spring 2016 Problem 8. Using the words \"slope\