y=40000(0.85)^x

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

1 answer

To fill out the table, we will calculate the value of the car using the function \( y = 40000(0.85)^x \) for different values of \( x \).

  1. For \( x = 0 \): \[ y = 40000(0.85)^0 = 40000(1) = 40000.00 \]

  2. For \( x = 1 \): \[ y = 40000(0.85)^1 = 40000(0.85) = 34000.00 \]

  3. For \( x = 3 \): \[ y = 40000(0.85)^3 = 40000(0.614125) \approx 24565.00 \]

  4. For \( x = 5 \): \[ y = 40000(0.85)^5 = 40000(0.443705) \approx 17748.20 \]

  5. For \( x = 8 \): \[ y = 40000(0.85)^8 = 40000(0.232630) \approx 9305.20 \]

Now, we can summarize the table values:

\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline 0 & 40000.00 \ 1 & 34000.00 \ 3 & 24565.00 \ 5 & 17748.20 \ 8 & 9305.20 \ \hline \end{array} \]

So the completed table is:

  • For \( x = 0 \): \( f(x) = 40000.00 \)
  • For \( x = 1 \): \( f(x) = 34000.00 \)
  • For \( x = 3 \): \( f(x) = 24565.00 \)
  • For \( x = 5 \): \( f(x) = 17748.20 \)
  • For \( x = 8 \): \( f(x) = 9305.20 \)