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.
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.
To solve this equation, we'll follow these steps:
Step 1: Distribute
Distribute 20000 to both terms inside the parentheses:
20000 - 800t = 13000
Step 2: Combine Like Terms
Combine the constants on the left side:
20000 - 13000 = 800t
7000 = 800t
Step 3: Solve for t
To isolate t, divide both sides of the equation by 800:
t = 7000 / 800
Step 4: Simplify the Result
Dividing 7000 by 800 gives us:
t ≈ 8.75
Therefore, the car will be worth $13,000 after approximately 8.75 years.