Question

y=40000(0.85)^x
ill out the table that represents the value of the car after x
𝑥
years. Do not include a comma in your response. Write your answer to the nearest cent, write ".00" if there are no cents.

x
𝑥
f(x)
𝑓
(
𝑥
)

0 $
1 $
3 $
5 $
8 $

Answer 1

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 \( x = 8 \): \( f(x) = 9305.20 \)