A vehicle purchased for 20700 depreciates at a constant rate

A vehicle purchased for $20700 depreciates at a constant rate of 17 % each year. Its value after t years can be modeled by the equation A = P(0.83)^t, where P is the original value of the vehicle. Determine the number of years that it takes for the vehicle to depreciate to $8000 Round to the nearest tenth. This is attempt 1 of 2.

Solution

A=P(0.83)^t

P=$20,700

A=8000

8000=20700(.83)^t

Taking log on both sides

log(8000/20700)=t log .83

t=5.1 years