In Exercises 105-108, you will be developing functions that...

In Exercises $105-108,$ you will be developing functions that model given conditions. A car was purchased for $\$ 22,500$. The value of the car decreased by $\$ 3200$ per year for the first six years. Write a function that describes the value of the car, $V,$ after $x$ years, where $0 \leq x \leq 6 .$ Then find and interpret $V(3)$

In Exercises $105-108,$ you will be developing functions that model given conditions.
A car was purchased for $\$ 22,500$. The value of the car decreased by $\$ 3200$ per year for the first six years. Write a function that describes the value of the car, $V,$ after $x$ years, where $0 \leq x \leq 6 .$ Then find and interpret $V(3)$

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Key Concepts

Linear Function

A linear function represents a constant rate of change between two variables and is typically written in the form f(x) = mx + b. In this representation, m signifies the constant rate of change (slope), and b signifies the initial value when x is zero. This concept is fundamental in modeling scenarios where a quantity changes uniformly over time.

Depreciation Model

A depreciation model uses a linear function to represent the decrease in value of an asset over time. When an asset loses value by a fixed amount per time interval, the relationship between time and value can be depicted as a linear function, making it easier to predict the asset's future value.

Domain of a Function

The domain of a function is the set of all possible input values for which the function is defined. In practical modeling, such as a depreciation model, the domain is often restricted to reflect the actual range of time or conditions under consideration, ensuring the model remains applicable to real-world contexts.

Function Evaluation

Function evaluation involves substituting a specific value for the independent variable in a function to determine the corresponding value of the dependent variable. This process is key in interpreting models, as it allows you to understand the effect of a particular moment or condition on the overall scenario.

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