You buy a car in 2005 for $7860 and it depreciates linearly. You sell the car for $5040 in 2011....
what does the domain represent in the function?
what does the range represent in this function?
what is the slope of the linear representation?
what is the function that models the linear representation?
using the model, make a prediction for what you could sell the car for today?
To answer these questions, we need to understand the concepts of domain, range, slope, and linear representation.
1. Domain: In this context, the domain represents the set of independent variables or inputs of the function. In other words, it represents the range of possible values for the year of purchase. The domain would be a time period, such as the years between 2005 and 2011.
2. Range: The range represents the set of dependent variables or outputs of the function. In this case, it represents the range of possible values for the price of the car. The range would consist of the different prices the car could be sold for.
3. Slope: The slope of a linear representation represents the rate of change or the rate at which one variable changes with respect to the other variable. In the context of this problem, the slope represents the rate at which the car depreciates per year.
4. Function: A linear function can be represented in the form of y = mx + b, where y represents the dependent variable (price), x represents the independent variable (year), m represents the slope, and b represents the y-intercept. The function that models the linear representation of the car's depreciation is y = -860x + b, where b is the initial value of the car (7860).
To make a prediction for what you could sell the car for today, we need to find the value of y (price) for the current year. However, you haven't provided the current year, so we cannot provide a specific prediction without that information.