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 motorcycle will have a value of $7000 after roughly 7.3 years
Statement 2 the motorcycle will have a value of $7000 after roughly 6.7 years
To graph the functions y=21000(1-0.15)^x and y=14000(1-0.09)^x using Geogebra:
1. Go to geogebra.org or open the Geogebra app.
2. Enter the functions into the input bar at the top of the screen: y=21000(1-0.15)^x and y=14000(1-0.09)^x
3. Click on the "New Worksheet" button to create a new worksheet.
4. Select the graphing tool and click on the graph to plot the functions.
5. Adjust the viewing window if necessary to see the full graph of the functions.
To determine when the motorcycle will be worth $7000, we can set up the equation 7000=14000(1-0.09)^x and solve for x:
7000 = 14000(1-0.09)^x
0.5 = (1-0.09)^x
0.5 = 0.91^x
Take the natural logarithm of both sides
ln(0.5) = ln(0.91)^x
x*ln(0.91) = ln(0.5)
x = ln(0.5) / ln(0.91)
x ≈ 6.7 years
Therefore, Statement 2 is correct, the motorcycle will be worth $7000 after roughly 6.7 years.