Here is what I need you to submit. Type a report that includes the following: 1. An introduction that gives an overview of this Investigation. 2. Answers to all the questions for You Try It 1 - 7. . Include any tables that you were asked to make. . Include all required graphs in the document. . Make graphs using Desmos (www.desmos.com). 3. Discussion: Post your You Try It #4 table and graph in the Investigation 2 Discussion forum. Reply to two other students. In your replies you can: . Ask students clarification questions . Share methods and strategies for making the graph and help each other with the process . Compare your caffeine consumption with that of your group members 4. Write a conclusion paragraph reflecting on the work you did, the math you used and your opinion of the investigation and the results that you got. Submit one file in pdf format by clicking Submit and uploading your file.Project 1.Introduction People consume caffeine in both food and drinks which comes from coffee, tea, kola nuts, mate, cocoa and guarana. People consume caffeine because of the taste while other do it for the physical effects it has. The effects of caffeine can be felt when sufficient amounts are present, which for most people is 32 to 200 mg caffeine to act as a minor stimulant. This project explores the dynamics of caffeine in the body through the use of exponential functions. Throughout, it displays the amount of caffeine in someone's body throughout time based on how much they consume. It shows the amount of time it takes to eliminate caffeine from your body and shows the average consumption of caffeine by recording your own consumption of caffeine. As seen in the project, caffeine affects the body in different ways. 2. Try It #1-7 You Try It #1 If a person starts the day by drinking 3 cups of coffee (one right after the other) containing 130 mg of caffeine each, assuming the caffeine is absorbed into the body immediately, a. How much caffeine will there be in this person's body 1 hour later? 2 hours later? 3 hours later? 0 hours: 390.0 mg 1 hour: 339.3 mg 2 hours: 295.2 mg 3 hours: 256.8 mg b. Reflect on how you computed the answers to part (a) to help you develop a simple expression that gives the amount of caffeine in this person's body 24 hours later, assuming no additional caffeine is consumed. Find the amount. 390(.87)^24 = 13.8mg You Try It #2 If a person starts the day by drinking 3 cups of coffee containing 130 mg of caffeine each, assuming the caffeine is immediately absorbed into the body, a. Write an equation in the form y = f(t) for the amount of caffeine in the body t hours after ingesting 390 mg. .87 4 f (t)=390 % 390 = initial caffeine starting point, t = total amount of hours b. Graph the function you developed in part (a). 400 390 caffeine 200 498.195 (12,25) 109 290 300 time (hours)c. What is the long term behavior ("end behavior") of the function you graphed? What does that say about the 390 mg of caffeine the person drank in the morning? As t - + 00 , f(t) - 0 In order for the caffeine to longer affect the body with the amount that was consumed it would take 17.95 hours. Also the greater the amount of caffeine that is taken in one time take a longer amount of time in order for the amount to reach 0. d. How much caffeine will be in the person's body 30 minutes after drinking 3 cups of coffee (when t = .5)? 8723=363.77 mg f (.5)=390 & e. How long will it take for the 390 mg of caffeine in the person's body to be reduced to 195 mg? 87 2 195=390 & t=log.87 (1/2) t=[log (1/2)]/(log .87) t=4.98 hrs You Try It #3 To understand half-life, first determine how much of the original 390 mg of caffeine is in the body after two half- lives; then after three half-lives. Then determine the value of t, time, for each of these answers. original = 4.98 hours 87 243 =194.93 c (4.98) = 390% 2 half-lives = 4.98(2) = 9.96 hrs 87 1936=97.43 mg c(9.96)=390 % 3 half-lives = 4.98(3) = 14.94 hrs 871= 48.69 mg c(14.94 )=3904 For every half-time which is equivalent to 4.98 hours that goes by, the amount remaining in the body is cut in half. You Try It #4 a. Make a table like the one at left to keep a record of your own caffeine consumption over a 24-hour period beginning when you wake in the morning. If you do not eat or drink caffeine, use data from a friend. Time of caffeine intake 8:00 am 10:30 am 1:00 pm 6:00 pm 9:30 pm 8:00 am Amount of caffeine in 91.78 100.09 59.85 73.61 21.76 body before consuming this caffeine Amount of caffeine in 130 50 20 60 15 90 this drink or food Amount of caffeine in 130 141.78 120.09 119.85 88.61 110.53 body after this intakeFunction that describes For For For For For the amount in caffeine For t224 Ost $2.5 2.5 st $5, 5sts 10, 10 sts 13.5 13.5 st$24 your body .87 21-24 .87 2 .8721-2.5 .872'-5 872t-10 .872-13.5 f (t)=130& f (t)=41.784 f (t)=120.094 f (t)=110.534 f (t)=119.854 f (t)=88.61% b. From your table, sketch a graph of the amount of caffeine in your body (or your friend's) over this 24-hour period. + +