A new car worth $21,000 is depreciating in value by $3000 per year. Complete parts (a) through (c). a. Write a formula that models the car's value, y, in dollars, after x years. b. Use the formula from part (a) to determine after how many years the car's value will be $6,000. c. Graph the formula from part (a) in the first quadrant of a rectangular coordinate system. Then, show your solution to part (b) on the graph. a. A formula that models the car's value, y, in dollars, after x years is b. After 5 years, the car's value will be $6,000. (Type a whole number.) c. Choose the correct graph below. O A. 21,000- 10 О в. Ay 10- 0- 21000 G (Type an equation.) O C.. 21,000 0- 10 Q OD. Ау 10- 0 21000 Q
A new car worth $21,000 is depreciating in value by $3000 per year. Complete parts (a) through (c). a. Write a formula that models the car's value, y, in dollars, after x years. b. Use the formula from part (a) to determine after how many years the car's value will be $6,000. c. Graph the formula from part (a) in the first quadrant of a rectangular coordinate system. Then, show your solution to part (b) on the graph. a. A formula that models the car's value, y, in dollars, after x years is b. After 5 years, the car's value will be $6,000. (Type a whole number.) c. Choose the correct graph below. O A. 21,000- 10 О в. Ay 10- 0- 21000 G (Type an equation.) O C.. 21,000 0- 10 Q OD. Ау 10- 0 21000 Q
Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Depreciation of a Car's Value over Time**
When you purchase a new car, its value typically decreases over time due to depreciation. This concept can be modeled mathematically and visually to help understand how a car’s worth diminishes year by year. Let’s explore this with an example and a few questions.
### Example:
A new car worth $21,000 is depreciating in value by $3,000 per year. Follow the steps below to analyze and graph the depreciation:
### Steps to Follow:
**a. Write a formula that models the car's value, \( y \), in dollars, after \( x \) years.**
To find the car's value \( y \) after \( x \) years, we use the formula:
\[ y = 21000 - 3000x \]
**b. Use the formula from part (a) to determine after how many years the car's value will be $6,000.**
To find after how many years the car's value will be $6,000, set \( y = 6000 \):
\[ 6000 = 21000 - 3000x \]
Solving for \( x \):
\[
6000 = 21000 - 3000x \\
3000x = 21000 - 6000 \\
3000x = 15000 \\
x = 5
\]
Hence, after 5 years, the car's value will be $6,000.
**c. Graph the formula from part (a) in the first quadrant of a rectangular coordinate system. Then, show your solution to part (b) on the graph.**
Below are four graph options. You need to choose the correct graph that accurately represents the depreciation model:
- **Option A:** Incorrect. This graph shows the value starting higher than $21,000 and decreasing at an incorrect rate.
- **Option B:** Incorrect. This graph incorrectly scales both axes.
- **Option C:** This graph correctly starts at $21,000 (when \( x = 0 \)) and shows a linear decrease in value. The point where \( x = 5 \) and \( y = 6000 \) is also correctly marked.
- **Option D:** Incorrect. This graph seems to depict a similar but incorrect scale and rate on both axes.
The correct choice is **Option C**.
### Explanation of Correct Graph:
- **](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66c67e03-2fde-4c21-adb6-231ac5c2058e%2F05dcbba9-860a-4b28-87d8-519c63805fd8%2Fhkbxz0a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Depreciation of a Car's Value over Time**
When you purchase a new car, its value typically decreases over time due to depreciation. This concept can be modeled mathematically and visually to help understand how a car’s worth diminishes year by year. Let’s explore this with an example and a few questions.
### Example:
A new car worth $21,000 is depreciating in value by $3,000 per year. Follow the steps below to analyze and graph the depreciation:
### Steps to Follow:
**a. Write a formula that models the car's value, \( y \), in dollars, after \( x \) years.**
To find the car's value \( y \) after \( x \) years, we use the formula:
\[ y = 21000 - 3000x \]
**b. Use the formula from part (a) to determine after how many years the car's value will be $6,000.**
To find after how many years the car's value will be $6,000, set \( y = 6000 \):
\[ 6000 = 21000 - 3000x \]
Solving for \( x \):
\[
6000 = 21000 - 3000x \\
3000x = 21000 - 6000 \\
3000x = 15000 \\
x = 5
\]
Hence, after 5 years, the car's value will be $6,000.
**c. Graph the formula from part (a) in the first quadrant of a rectangular coordinate system. Then, show your solution to part (b) on the graph.**
Below are four graph options. You need to choose the correct graph that accurately represents the depreciation model:
- **Option A:** Incorrect. This graph shows the value starting higher than $21,000 and decreasing at an incorrect rate.
- **Option B:** Incorrect. This graph incorrectly scales both axes.
- **Option C:** This graph correctly starts at $21,000 (when \( x = 0 \)) and shows a linear decrease in value. The point where \( x = 5 \) and \( y = 6000 \) is also correctly marked.
- **Option D:** Incorrect. This graph seems to depict a similar but incorrect scale and rate on both axes.
The correct choice is **Option C**.
### Explanation of Correct Graph:
- **
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