### Depreciation Problem **Problem Statement:** A car is purchased for $43,000. Each year it loses 30% of its value. After how many years will the car be worth $8900 or less? (Use the calculator provided if necessary.) Write the **smallest possible whole number** answer. **Input Box:** - Enter the number of years. --- **Note:** This problem involves calculating the depreciation of the car's value over time. Depreciation is evaluated based on the formula for exponential decay: \[ V = P \times (1 - r)^t \] Where: - \( V \) is the final value, - \( P \) is the initial purchase price, - \( r \) is the rate of depreciation (as a decimal), - \( t \) is the time in years. In this problem: - \( P = 43,000 \) - \( r = 0.30 \) - \( V \leq 8,900 \) The goal is to solve for the smallest integer \( t \) where the condition is met. **Solution Strategy:** 1. Start by inserting different values of \( t \). 2. Calculate the value using the formula until the car's value is $8900 or less. 3. Input the smallest \( t \) in the provided box. **Buttons:** - Explanation: View the method and steps to reach the solution. - Check: Verify the entered answer.
### Depreciation Problem **Problem Statement:** A car is purchased for $43,000. Each year it loses 30% of its value. After how many years will the car be worth $8900 or less? (Use the calculator provided if necessary.) Write the **smallest possible whole number** answer. **Input Box:** - Enter the number of years. --- **Note:** This problem involves calculating the depreciation of the car's value over time. Depreciation is evaluated based on the formula for exponential decay: \[ V = P \times (1 - r)^t \] Where: - \( V \) is the final value, - \( P \) is the initial purchase price, - \( r \) is the rate of depreciation (as a decimal), - \( t \) is the time in years. In this problem: - \( P = 43,000 \) - \( r = 0.30 \) - \( V \leq 8,900 \) The goal is to solve for the smallest integer \( t \) where the condition is met. **Solution Strategy:** 1. Start by inserting different values of \( t \). 2. Calculate the value using the formula until the car's value is $8900 or less. 3. Input the smallest \( t \) in the provided box. **Buttons:** - Explanation: View the method and steps to reach the solution. - Check: Verify the entered answer.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Depreciation Problem
**Problem Statement:**
A car is purchased for $43,000. Each year it loses 30% of its value. After how many years will the car be worth $8900 or less? (Use the calculator provided if necessary.)
Write the **smallest possible whole number** answer.
**Input Box:**
- Enter the number of years.
---
**Note:**
This problem involves calculating the depreciation of the car's value over time. Depreciation is evaluated based on the formula for exponential decay:
\[ V = P \times (1 - r)^t \]
Where:
- \( V \) is the final value,
- \( P \) is the initial purchase price,
- \( r \) is the rate of depreciation (as a decimal),
- \( t \) is the time in years.
In this problem:
- \( P = 43,000 \)
- \( r = 0.30 \)
- \( V \leq 8,900 \)
The goal is to solve for the smallest integer \( t \) where the condition is met.
**Solution Strategy:**
1. Start by inserting different values of \( t \).
2. Calculate the value using the formula until the car's value is $8900 or less.
3. Input the smallest \( t \) in the provided box.
**Buttons:**
- Explanation: View the method and steps to reach the solution.
- Check: Verify the entered answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0bdd0630-6d91-4a56-9e6c-bfe7696b31b2%2F3a21ee79-19f5-46cf-8bc0-799b2f1571d8%2F7dgtdan.jpeg&w=3840&q=75)
Transcribed Image Text:### Depreciation Problem
**Problem Statement:**
A car is purchased for $43,000. Each year it loses 30% of its value. After how many years will the car be worth $8900 or less? (Use the calculator provided if necessary.)
Write the **smallest possible whole number** answer.
**Input Box:**
- Enter the number of years.
---
**Note:**
This problem involves calculating the depreciation of the car's value over time. Depreciation is evaluated based on the formula for exponential decay:
\[ V = P \times (1 - r)^t \]
Where:
- \( V \) is the final value,
- \( P \) is the initial purchase price,
- \( r \) is the rate of depreciation (as a decimal),
- \( t \) is the time in years.
In this problem:
- \( P = 43,000 \)
- \( r = 0.30 \)
- \( V \leq 8,900 \)
The goal is to solve for the smallest integer \( t \) where the condition is met.
**Solution Strategy:**
1. Start by inserting different values of \( t \).
2. Calculate the value using the formula until the car's value is $8900 or less.
3. Input the smallest \( t \) in the provided box.
**Buttons:**
- Explanation: View the method and steps to reach the solution.
- Check: Verify the entered answer.
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