Question

se the table to answer the question.

Years, x Value of Car, f(x)
1 29, 750.00
2 25, 287.50
3 21, 494.38
4 18, 270.22
5 ?
A car decreases in value after a given number of years. The following function represents the value of the car in dollars with respect to its age, x, in years: f(x)=35,000(.85)x . Use the input-output table to determine the value of the car after 5 years. Round your answer to the nearest cent.

(1 point)
Rounded to the nearest cent, after 5 years, the value of the car will equal $
.
Remaining Attempts : 3
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Answer 1

wrong

Answer 2

A car decreases in value after a given number of years. The following function represents the value of the car in dollars with respect to its age, x, in years: f(x)=35,000(.85)^x . Use the input-output table to determine the value of the car after 5 years. Round your answer to the nearest cent.

Answer 3

To determine the value of the car after 5 years using the given function \( f(x) = 35,000 \cdot (0.85)^x \), we need to substitute \( x \) with 5.

Let's calculate \( f(5) \):

\[
f(5) = 35,000 \cdot (0.85)^5
\]

Now let's compute \( (0.85)^5 \):

\[
(0.85)^5 \approx 0.4437053125
\]

Next, we multiply this result by 35,000:

\[
f(5) = 35,000 \cdot 0.4437053125 \approx 15529.64659375
\]

Now, rounding to the nearest cent, we get:

\[
f(5) \approx 15,529.65
\]

Thus, the value of the car after 5 years will be approximately **$15,529.65**.

Answer 4

Let's carefully recalculate the value of the car after 5 years using the function \( f(x) = 35,000 \cdot (0.85)^x \).

1. Plug in \( x = 5 \):
\[
f(5) = 35,000 \cdot (0.85)^5
\]

2. Calculate \( (0.85)^5 \):
\[
(0.85)^5 \approx 0.4437053125
\]

3. Multiply by 35,000:
\[
f(5) = 35,000 \cdot 0.4437053125 \approx 15,529.64609375
\]

4. Round to the nearest cent:
\[
f(5) \approx 15,529.65
\]

So based on my calculations, the value of the car after 5 years is indeed approximately **$15,529.65**.

If you believe there's a mistake or think the answer should be different, please provide any additional information or clarify any constraints I'm missing!

Answer 5

Let’s calculate the value of the car after 5 years again using the formula \( f(x) = 35,000 \cdot (0.85)^x \).

1. Substitute \( x \) with 5:
\[
f(5) = 35,000 \cdot (0.85)^5
\]

2. Calculate \( (0.85)^5 \):
\[
(0.85)^5 \approx 0.4437053125
\]

3. Now, multiply this value by 35,000:
\[
f(5) = 35,000 \cdot 0.4437053125 \approx 15,529.64609375
\]

4. Finally, round this to the nearest cent:
\[
f(5) \approx 15,529.65
\]

Thus, the value of the car after 5 years is approximately **$15,529.65**. If there’s a specific calculation you want me to address differently, please let me know!