Unit Activity Unit: Functions This activity will help you meet these educational goals: Mathematical PracticesYou will make sense of problems and solve them, reason abstractly and quantitatively, construct viable arguments and critique the reasoning of others, use mathematics to model real-world situations, look for and make use of structure, and look for and express regularity in repeated reasoning. Introduction In this unit, you learned how to create, use, and compare functions. In this activity, you will analyze and compare real-world situations by modeling them as functions. __________________________________________________________________________ Directions and Analysis Task 1: Saving for Vacation Jerry plans to begin saving money for a trip by putting $1 in a savings account the first month and then adding enough to double the amount in the account each following month. 1 2014 EDMENTUM, INC. a. After he finishes contributing to the account, he will withdraw $500 to make a down payment on the trip. Create a function to show how much money will be in the account if he finishes contributing to the account after t months. Type your response here: b. Jerry plans to keep up this saving pattern until he can no longer afford it. At that time, he hopes to have enough in his account for his trip. How much will be in the account, after making the down payment, if the most he will be able to contribute in a month is $1,200? Type your response here: c. Jerry's friend Brandon is planning to start saving for a trip at the same time as Jerry. The graph shows the balance in Brandon's account over the first few months of saving. Whose account will have the greatest balance after the first five months of savings, Brandon's or Jerry's? Type your response here: d. How long will it take for the person with the smaller account balance after five months to have the greater balance? Type your response here: e. Brandon will also need to withdraw $500 to make a down payment on the trip. How much will be in Brandon's account, after making the down payment, if he contributes for the 2 same amount of time as Jerry? (Review your calculation in part b to determine how long Jerry continued his savings plan.) Type your response here: Task 2: Driving Jerry is driving to his vacation destination. He decided to keep track of the distance to his destination after different amounts of times spent driving. He created a table from the data he collected. Hours Spent Driving Miles to Destination 1 1,259 5 999 6 934 9 739 a. Assuming that the pattern is the same for Jerry's entire drive to his destination, create a function to represent the distance remaining to his destination based on the number of hours, h, he has driven. Type your response here: b. What is the domain of this function in the context of the problem? Explain. Type your response here: c. What is the range of this function in the context of the problem? Explain. Type your response here: 3 d. When Jerry recorded the last entry in the table (9 hours driven, 739 miles to go), how much longer did he need to drive to arrive at his destination? Type your response here: e. Write the function you created in part a as a recursive function. Type your response here: f. How would a recursive function be more useful in this situation than a normal function? Type your response here: __________________________________________________________________________ Resources Document any references you used for this project below. At minimum, include a title and URL for any Internet resource: 4 Evaluation Your teacher will use this rubric to evaluate the completeness of your work as well as the clarity of thinking you exhibit. Total Points: 10 Task 1: Saving for Vacation Task points: 5 a. Create a function. 1 b. Find the amount in Jerry's account after the down payment. 1 c. Determine whose account has the higher balance after five months. 1 d. Find how long it would take for the person with the lower account balance to have the higher account balance. 1 e. Find the amount in Brandon's account after the down payment. 1 Task 2: Driving Task points: 5 a. Create a function. 1 b. Find the domain of the function. 0.5 c. Find the range of the function. 0.5 d. Find how much longer it will take to reach the destination. 1 e. Write a recursive function. 1 f. Explain when a recursive function would be more helpful. 5 1