To determine the correct answer, let’s analyze the given problem step by step:

We know the following from the problem:

• The price $P$ of a car is a linear function of its age $t$.
• $P(4) = 7300$ and $P(7) = 5500$.

Step 1: Find the rate of change (slope)

The rate of change (or slope $m$) of a linear function is given by: $m = \frac{\Delta P}{\Delta t} = \frac{P(7) - P(4)}{7 - 4}.$

Substitute the known values: $m = \frac{5500 - 7300}{7 - 4} = \frac{-1800}{3} = -600.$

Thus, the price decreases by $600 per year.

Step 2: Interpret the result

The negative slope $-600$ means that for each additional year of age, the car's price decreases by approximately $600.

Step 3: Verify the options

• Option A: Decreases by 25% → Incorrect (percentage not relevant here).
• Option B: Decreases by 75% → Incorrect.
• Option C: Decreases by approximately $600 → Correct.
• Option D: Decreases by $1800 → Incorrect.

Final Answer:

The correct option is C: For each year that a car ages, its price decreases by approximately $600.

Do you want me to explain further or solve any related questions?

Here are 5 related questions to consider:

1. How do you write the full equation of the linear function $P(t)$ for this problem?
2. If a car is 10 years old, what would its price be based on this model?
3. How do you calculate the percentage decrease per year for this model?
4. Can you verify the intercept of the linear function $P(t)$?
5. What is the significance of the slope and y-intercept in this context?

Tip: Always check units and interpret the slope carefully when dealing with word problems involving linear functions.