Asked by Jane

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.

Answers

Answered by Reiny
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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