Posted by **Jane** on Wednesday, April 11, 2012 at 10:07pm.

Please show me how to solve:

The value of a $20,000 car decreases every year, t. The equation below models this situation:

20000(1-0.04t)=13,000.

After how many years will the car be worth $13,000. Round to the nearest tenth if necessary.

- Algebra I -
**Reiny**, Wednesday, April 11, 2012 at 10:27pm
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.

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