From the image you provided, the problem seems to involve a linear function, $P(t)$, that models the price of a used car based on its age, $t$, in years. Specifically, it is known that:

$P(1) = 7300 \quad \text{and} \quad P(7) = 5300.$

You are asked to determine which statement best describes how the price decreases per year.

Solution:

Since this is a linear function, the price decreases by the same amount each year, which means the slope $m$ of the function $P(t)$ is constant.

To find the slope $m$, we can use the slope formula for a linear function:

$m = \frac{P(7) - P(1)}{7 - 1} = \frac{5300 - 7300}{7 - 1} = \frac{-2000}{6} = -333.33$

This means the price of the car decreases by approximately $333.33 per year.

The correct answer in the image corresponds to the statement: "For each year that a car ages, its price decreases by approximately $333."

Would you like further details on how linear models work or have any questions?

Related Questions:

1. How would the linear model change if the car's price increases with age?
2. How do you interpret the slope in other real-life contexts?
3. Can a linear function ever model a car's value increasing over time?
4. What happens to the function $P(t)$ if we model a faster depreciation rate?
5. How would this problem change if you had a different type of function, like quadratic depreciation?

Tip:

Linear functions are a great way to model constant rates of change, but always check if your situation involves constant or changing rates!