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.
I was instructed that the answer is
t = 8.75. How do I set it up and solve it?
13000/20000=(1-0.04t)
(13000/20000)-1=-0.04t
[(13000/20000)-1]/-0.04=t
t=8.75
Are you sure the equation wasn't
20000(1 - .04)^t = 13000 ?
That would be the usual way to express a depreciation of 4% per year.
In that case ....
(.96)^t = .65
log (.96^t) = log .65
t log .96 = lot .65
t = log ..5/log .96 = 10.55
If however, the equation is as you typed it, then go with Tom's answer, it is correct.
PS
If you look at the "related questions" below, you have asked this question several times, it has been correctly answered, but for some reason you are not accepting the correct answer.
To solve this equation, we need to isolate the variable t. Here are the steps to set up and solve it:
1. Start with the given equation: 20000(1 - 0.04t) = 13000.
2. Divide both sides of the equation by 20000 to get rid of the coefficient: (1 - 0.04t) = 13000/20000.
Simplifying the right side gives: (1 - 0.04t) = 0.65.
3. Rewrite the equation as: 1 - 0.04t = 0.65.
4. Move the constant term to the right side by subtracting 1 from both sides: -0.04t = 0.65 - 1.
Simplifying the right side further gives: -0.04t = -0.35.
5. Now, divide both sides of the equation by -0.04 to solve for t: t = (-0.35)/(-0.04).
Dividing -0.35 by -0.04 gives: t = 8.75.
Hence, after approximately 8.75 years, the car will be worth $13,000.
To set up and solve the equation, you need to isolate the variable t on one side of the equation. Here's how you can do it step by step:
1. Start with the equation: 20000(1 - 0.04t) = 13,000.
2. Begin by distributing 20000 to both terms inside the parentheses: 20000 - 800t = 13,000.
3. Next, subtract 20000 from both sides of the equation to isolate the term with t: -800t = 13,000 - 20,000.
Simplify this to: -800t = -7,000.
4. Divide both sides of the equation by -800 to solve for t: t = (-7,000) / (-800).
This simplifies to: t = 8.75.
Therefore, after approximately 8.75 years, the car will be worth $13,000.