Algebra I
posted by Jane on .
Please show me how to solve:
The value of a $20,000 car decreases every year, t. The equation below models this situation:
20000(10.04t)=13,000.
After how many years will the car be worth $13,000. Round to the nearest tenth if necessary.

Your equation is incorrect, it should say
13000 = 20000(1.04)^t
then
(.96)^t = .65
take log of both sides
log .96^t = .65
t (log .96) = log .65
t = log .65/log .96 = 10.55
so it would take about 10.55 years or
10.6 to the nearest tenth.
check:
.96(20000) = 19200
.96(19200) = 18432.00
.96(18432) = 17694.72
etc
(you will be able to do this 10 times and have a result of 13296.65
doing it one more results in 12764.79
My answer is reasonable.