Question
Use 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 $
.
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 $
.
Answers
Answer
wrong
Answered by
GPT-4o mini
To find the value of the car after 5 years using the function \( f(x) = 35,000(0.85)^x \), we can substitute \( x = 5 \) into the equation:
\[
f(5) = 35,000(0.85)^5
\]
First, we calculate \( (0.85)^5 \):
\[
(0.85)^5 \approx 0.4437053125
\]
Now, multiply this value by 35,000:
\[
f(5) = 35,000 \times 0.4437053125 \approx 15529.675
\]
Now, rounding this to the nearest cent:
\[
f(5) \approx 15,529.68
\]
Therefore, rounded to the nearest cent, after 5 years, the value of the car will equal **$15,529.68**.
\[
f(5) = 35,000(0.85)^5
\]
First, we calculate \( (0.85)^5 \):
\[
(0.85)^5 \approx 0.4437053125
\]
Now, multiply this value by 35,000:
\[
f(5) = 35,000 \times 0.4437053125 \approx 15529.675
\]
Now, rounding this to the nearest cent:
\[
f(5) \approx 15,529.68
\]
Therefore, rounded to the nearest cent, after 5 years, the value of the car will equal **$15,529.68**.
Answered by
GPT-4o mini
Let's recalculate the value of the car after 5 years using the function \( f(x) = 35,000(0.85)^x \) more carefully.
1. We need to find \( f(5) = 35,000(0.85)^5 \).
First, calculate \( (0.85)^5 \):
\[
(0.85)^5 = 0.85 \times 0.85 \times 0.85 \times 0.85 \times 0.85
\]
Calculating this step-by-step:
\[
0.85^2 = 0.7225
\]
\[
0.85^3 = 0.7225 \times 0.85 \approx 0.614125
\]
\[
0.85^4 = 0.614125 \times 0.85 \approx 0.52191875
\]
\[
0.85^5 = 0.52191875 \times 0.85 \approx 0.4437053125
\]
Now, multiply by 35,000:
\[
f(5) = 35,000 \times 0.4437053125 \approx 15529.675
\]
This calculation indicates the result is approximately:
\[
f(5) \approx 15,529.68
\]
If you believe there is an error, let's double-check the calculations:
\((0.85)^5\) can also be computed directly using a calculator:
\[
0.85^5 \approx 0.443705
\]
Thus,
\[
35,000 \times 0.443705 \approx 15529.675
\]
When rounded to the nearest cent, this is indeed:
\[
f(5) = 15,529.68
\]
If there's a specific aspect of the calculation that you'd like me to clarify further or if you have other information, please let me know!
1. We need to find \( f(5) = 35,000(0.85)^5 \).
First, calculate \( (0.85)^5 \):
\[
(0.85)^5 = 0.85 \times 0.85 \times 0.85 \times 0.85 \times 0.85
\]
Calculating this step-by-step:
\[
0.85^2 = 0.7225
\]
\[
0.85^3 = 0.7225 \times 0.85 \approx 0.614125
\]
\[
0.85^4 = 0.614125 \times 0.85 \approx 0.52191875
\]
\[
0.85^5 = 0.52191875 \times 0.85 \approx 0.4437053125
\]
Now, multiply by 35,000:
\[
f(5) = 35,000 \times 0.4437053125 \approx 15529.675
\]
This calculation indicates the result is approximately:
\[
f(5) \approx 15,529.68
\]
If you believe there is an error, let's double-check the calculations:
\((0.85)^5\) can also be computed directly using a calculator:
\[
0.85^5 \approx 0.443705
\]
Thus,
\[
35,000 \times 0.443705 \approx 15529.675
\]
When rounded to the nearest cent, this is indeed:
\[
f(5) = 15,529.68
\]
If there's a specific aspect of the calculation that you'd like me to clarify further or if you have other information, please let me know!
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