A new car worth 24,000 is depreciating in value by 3000...

A new car worth $\$ 24,000$ is depreciating in value by $\$ 3000$ per year.
a. Write a formula that models the car's value, $y,$ in dollars, after $x$ years.
b. Use the formula from part (a) to determine after how many years the car's value will be $\$ 9000$ .

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Key Concepts

Depreciation

Depreciation is the process of decreasing the value of an asset over time, often modeled with a fixed amount or a percentage loss per time period. This concept is essential in understanding how assets such as vehicles lose value over the years.

Linear Functions

A linear function represents a straight-line relationship between two variables. It is typically expressed in the form y = mx + b, where m is the slope (indicating the rate of change) and b is the y-intercept (indicating the starting value). This concept is useful for modeling constant changes over time.

Slope-Intercept Form

The slope-intercept form is a way of writing the equation of a line as y = mx + b. It clearly shows the initial value of the function and how the value changes over time, which is particularly useful in real-world applications involving constant rates of increase or decrease.

Solving Linear Equations

Solving linear equations involves finding the value of the variable that satisfies the equation. This process is crucial when determining the time or number of periods required for a value to reach a certain level, as seen in scenarios where a modeled quantity depreciates or appreciates to a specific amount.

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