From the image, I can see a question involving the market value of a home, and the student is asked to create and solve an equation to determine the year when the market value reaches a specific amount.

The given information includes:

• Initial market value in 2012: $330,000$
• The home’s market value increases by $7,500 every year.
• You are asked to find the year when the value of the home will be $486,000.

Setting up the equation:

Let $y$ represent the number of years since 2012, and let $V$ be the market value of the home in a given year. We know:

• The initial value in 2012 is $330,000.
• The value increases by $7,500 each year.

The equation for the market value $V$ after $y$ years is:

$V = 330,000 + 7,500 \cdot y$

You are tasked with finding $y$ when the market value $V$ reaches $486,000. So, substitute $V = 486,000$ into the equation:

$486,000 = 330,000 + 7,500 \cdot y$

Solving for $y$:

1. Subtract $330,000 from both sides: $486,000 - 330,000 = 7,500 \cdot y$ $156,000 = 7,500 \cdot y$

2. Divide both sides by 7,500: $y = \frac{156,000}{7,500}$ $y = 20.8$

Since $y$ represents the number of years, we round 20.8 to the nearest whole number, so $y \approx 21$.

Final Answer:

The home will reach a market value of $486,000 approximately 21 years after 2012, which is the year 2033.

Would you like further details or have any other questions?

Here are five related questions:

1. How would the equation change if the home’s value increased by a different amount each year?
2. If the home’s value started at a different base amount in 2012, how would the solution process change?
3. Can you find the market value of the home in the year 2025 based on the same growth rate?
4. What if the rate of increase in market value decreased after a certain number of years?
5. How could you graph the equation $V = 330,000 + 7,500y$ to visually represent the market value over time?

Tip: Always double-check rounding in final answers, especially when the variable represents years or other real-world units.