Assignment 58
This should make sense. If a quantity loses 2% a year, then for any year, you should have 98% of what you had the previous year. We can ask questions like:
======================================================== The table below relates to finance (previous assignment):
Problem: A purchased item loses 11% of its value each year. The purchase price was $4,000. (a) What will be the value of the item after 5 years? Solution (with communication): (a) $4,000(1- 0.11)^{5} = $4,000(0.89)^{5} = $2,233.62. (b) We need to solve $4,000(0.89^{x}) = $1,000 ==> 0.89^{x} = 0.25. By trial and error (possibly using the TABLE feature on your calculator) we find the 0.89^{11} = 0.27752 and 0.89^{12} = 0.24699. We conclude it will take 12 years for the value to decrease to $1,000. Problem: An item valued at $1,000 increases in value by 6% a year. Another item valued at $5,000 decreases in value by 8% year. After how many years will the items have equal value, and what is that value? Solution (with communication): If x is the number of years requested, then we must solve $1,000(1.06)^{x} = $5,000(0.92)^{x } Using the TABLE feature on the calculator, we find that at x = 11, the values (to the nearest dollar) are $1,898 and $1,998 respectively. At x = 12, the respective values are $2,012 and $1838. So, a reasonable response would be that both would have a value of approximately $1,940 after 11 years. If we use the calculator for a very accurate graphics solution, we would find that both values are $1,938.77 when x = 11.36. |