https://file.aiquickdraw.com/mathbot/file/1726804546424sigv4zsy.jpg

Let's solve this problem step by step.

The house was initially purchased for **$140,000**, and after 3 years, its value increased to **$155,000**. The value increase is linear, meaning that the change in value happens at a constant rate over time. We are asked to determine the formula that represents the house's value $ V $ after $ t $ years from the purchase.

### Step 1: Find the rate of increase per year
- The value increased from **$140,000** to **$155,000** over 3 years.
- The total increase is:
  \[
  155,000 - 140,000 = 15,000 \text{ dollars}
  \]
- The rate of increase per year is:
  \[
  \frac{15,000}{3} = 5,000 \text{ dollars per year}
  \]

### Step 2: Write the linear equation
The linear model for the house's value after $ t $ years is of the form:
\[
V = 140,000 + ( \text{rate} \times t )
\]
Using the rate of increase $ 5,000 $ dollars per year:
\[
V = 140,000 + 5,000t
\]

### Step 3: Analyze the options
- The correct equation is $ V = 140,000 + 5,000t $.
- This matches the first option in the list.

### Final Answer:
The correct choice is the first equation: 
\[
V = 140,000 + 5,000t
\]

Would you like more details on this process or any further clarification?

Here are 5 related questions to explore:
1. How would the equation change if the house’s value had increased at a faster rate?
2. What if the value of the house had decreased linearly instead? How would the equation look?
3. Can you derive a general formula for any linear growth problem?
4. How can we graph this equation, and what would the graph look like?
5. How would the equation change if the house’s value increased non-linearly?

**Tip:** When dealing with word problems involving rates of change, always identify the rate per unit (e.g., dollars per year) to set up your equation.

A house was purchased for $140,000. Three years later, the value of the house was $155,000. If the value V of the house increased linearly from the date it was purchased, which of the following represents the value, in dollars, of the house t years after the date it was purchased?

Learn how to solve a linear growth problem involving the increase in the value of a house. The house was purchased for $140,000, and three years later its value was $155,000. Find the linear equation that represents the house's value over time. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation