Salim purchases a new car for $21,000, and it depreciates in value each year. The function y = 21, 000(1 - 0.15)^x represents the depreciation. He also purchases a motorcycle, which depreciates each year as well. Its depreciation is represented by the function y = 14, 000(1 - 0.09)^x. Graph these two functions using GeoGebra. Which statement best describes when the car will be worth $4,000?

Question

Salim purchases a new car for $21,000, and it depreciates in value each year. The function y = 21, 000(1 - 0.15)^x represents the depreciation. He also purchases a motorcycle, which depreciates each year as well. Its depreciation is represented by the function y = 14, 000(1 - 0.09)^x. Graph these two functions using GeoGebra. Which statement best describes when the car will be worth $4,000?

Statement #1: The car will have a value of $4,000 after roughly 10.2 years.
Statement #2: The car will have a value of $4,000 after roughly 13.3 years.

Answer 1

To graph the functions in GeoGebra and determine when the car will be worth $4,000, follow these steps:

1. Open GeoGebra and enter the first function in the input bar: y = 21000(1 - 0.15)^x
2. Enter the second function in the input bar: y = 14000(1 - 0.09)^x
3. Adjust the viewing window to see the depreciation over time for both the car and the motorcycle.
4. Look for when the car's value reaches $4,000 on the y-axis.

After plotting the functions and analyzing the graphs, it can be seen that the car will have a value of $4,000 after roughly 10.2 years. Therefore, Statement #1 is accurate.