4-5 Applications Name We'll begin this assignment by looking at the savings plan for Joe, a 10-year-old with a seady job making $30.000 a year, with an annual raise of 49. Looking ahead to the future, Joe commits to saving 125 of his earnings every year. He chooses a fixed Tund investment that returns 9 annually. The following graph shows Joe's earnings, the amount of money he spends, and the amount of money that is generated in interest on his investment cach year. The purple curve isn't the amount he's saved; it's the amount of interest earned each year. The values on the xaxis represent Joe's age in years. SI SIX SIDO S . 500.000,00 Age The investment income graph displays the true magic of exponential growth: The income is limited when Joe's a young guy. but as he gets closer to thinking about retirement, the income really takes off. Notice that at age 65, something awesome hap- pens: The income that Joe's making from his investments is more than his living expenses. At that point, he can retire and live as well as ever without you know, working for a living. Sweet! This age is known in financial circles as the crossover point Use the information provided to answer Questions 1-5 1. How much money is Joe earning when he's 30? How much money is he allowing himself to spend when he's 207 Show i calculation, then describe whether or not your answer seems correct based on the graph. 4-5 Applications Name 3. How much is Joe earning when he's 357 Show a calculation based on the annual relative growth rate of 4%. Then describe whether or not your answer seems correct based on the graph. 4. How much money is Joe allowing himself to spend when he's 35? Show a calculation, then describe whether or not your answer seems correct based on the graph. 5. Carefully explain the meaning of the crossover point. Now turn your attention to the graph to answer Questions 6-8. 6. How much is Joe earning in salary when he's 60? 7. How much is Joe allowing himself to spend when he's 60? 4-5 Applications Name 8. How much is Joe earning from his investments at 60? 9. Write a function of the form "FX) expression where the expression describes the amount Joe carns x years after ape 30. If you need guidance, look at the answers to Applications Question 3 and Class Question 6 10. Use your answer to Question 9 to find how much Joe earns at age 60. How does it compare to the estimate you got from the graph? 11. Write a function of the form expression where the expression describes the amount Joe spends x years after age 30 12. Use your answer to Question 11 to find how much Joe spends at age 60. How does it compare to the estimate you got from the graph
