A new car is purchased for 17900 dollars. The value of the car depreciates at 13% per year. What will the value of the car be, to the nearest cent, after 7 years?
Each year, the value of the car decreases by 13% of its current value. So after 1 year, the value is 100% - 13% = 87% of the original value.
After 2 years, the value is 87% of 87% = 87%^2 of the original value.
After 3 years, the value is 87% of 87% of 87% = 87%^3 of the original value.
After 7 years, the value is 87%^7 of the original value.
87% is the same as 0.87.
0.87^7 ≈ 0.3897.
So after 7 years, the value of the car will be 0.3897 times the original value: 17900 * 0.3897 = $6967.30. Answer: \boxed{6967.30}.