ill out the table that represents the value of the car after x

Question

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years. Do not include a comma in your response. Write your answer to the nearest cent, write ".00" if there are no cents.

x
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f(x)
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(
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0 $
1 $
3 $
5 $
8 $

Answer 1

To complete the table representing the value of a car after x years, typically, we would use a formula for depreciation. A common model for car depreciation is that a car loses a fixed percentage of its value each year. For this example, let's assume the car starts with an initial value of $20,000 and depreciates at a rate of 15% per year.

Using the formula for depreciation:

$$f(x)=P(1-r{)}^x$$

where:

• $P$ is the initial value of the car (here, $20000$),
• $r$ is the rate of depreciation (15% or 0.15),
• $x$ is the number of years.

Let's calculate $f(x)$ for different values of $x$:

1. For $x=0$: $$f(0)=20000\times (1-0.15{)}^0=20000\times 1=20000.00$$

2. For $x=1$: $$f(1)=20000\times (1-0.15{)}^1=20000\times 0.85=17000.00$$

3. For $x=3$: $$f(3)=20000\times (1-0.15{)}^3=20000\times {0.85}^3\approx 20000\times 0.614125=12282.50$$

4. For $x=5$: $$f(5)=20000\times (1-0.15{)}^5=20000\times {0.85}^5\approx 20000\times 0.443705=8874.10$$

5. For $x=8$: $$f(8)=20000\times (1-0.15{)}^8=20000\times {0.85}^8\approx 20000\times 0.272490=5449.80$$

Now we can fill out the table:

$$\text{Misplaced hline}$$

The completed values are:

• For $x=0$: $20000.00
• For $x=1$: $17000.00
• For $x=3$: $12282.50
• For $x=5$: $8874.10
• For $x=8$: $5449.80