salim purchased a new car for $21000 and it depreciates in value each year the function y=21000(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=14000(1-0.09)^x graph these two functions using geogebra which statement best describes when the motorcycle will be worth $7000
Statement 1 the car will have a value of $4000 after roughly 10.2 years
Statement 2 the car will have a value of $4000 after roughly 13.3 years
To graph the two functions in GeoGebra, you can follow these steps:
1. Go to the GeoGebra website or open the GeoGebra app.
2. Click on the "Graphing" tab to open a new graphing window.
3. Enter the first function y=21000(1-0.15)^x in the input bar at the top of the window and press Enter.
4. Enter the second function y=14000(1-0.09)^x in the same input bar and press Enter.
5. The two functions should now be graphed on the same set of axes.
To determine when the motorcycle will be worth $7000, you can set up an equation with the second function and solve for x:
14000(1-0.09)^x = 7000
(1-0.09)^x = 0.5
Taking the logarithm of both sides, you get:
x*log(1-0.09) = log(0.5)
x = log(0.5) / log(1-0.09)
Using a calculator to evaluate the expression, x is approximately 7.62 years.
Therefore, the best statement that describes when the motorcycle will be worth $7000 is:
Statement 2: the car will have a value of $4000 after roughly 13.3 years.