Interpreting Graphs: We Often Use Graphs Of Recent Data

interpreting Graphs We Often Use Graphs Of Recent Data To Projec

1. Interpreting Graphs: We often use graphs of recent data to project the changes in future data. The following is the graph of a car’s value. The car was bought for $20,000. Each year, the car’s value decreases $2,800.

We can use this to project what the worth of the car will be if we ever decide to sell it.

a. Write a formula to model the car’s value, where “y” is the value of the car and “x” is the number of years.

b. Find the value of the car algebraically after five years. Does this match the graph above?

Paper For Above instruction

The process of interpreting graphs, especially those depicting quantitative data over time, is fundamental in projecting future trends and making informed decisions. In this context, the graph of a car’s value over time provides a visual and mathematical basis for understanding depreciation - a common phenomenon in asset valuation.

To construct an accurate model for the car’s value, we analyze the given data points: the initial value of the car and its annual rate of depreciation. The car was purchased for $20,000, and its value decreases by $2,800 each year. This information indicates a linear relationship between time and value, which can be described mathematically using a linear equation.

The general form of a linear equation modeling this relationship is: y = mx + b, where y represents the value of the car, x indicates the number of years since purchase, m is the slope (rate of change), and b is the y-intercept (initial value).

Given that the car depreciates by $2,800 annually, the slope (m) is negative: m = -2800. The initial value when x = 0 (at the time of purchase) is $20,000, which is the y-intercept: b = 20000. Therefore, the specific formula becomes:

y = -2800x + 20000

This formula allows us to calculate the car’s value at any year x by substituting the appropriate value into the equation.

To find the value of the car after five years, substitute x = 5 into the formula:

y = -2800(5) + 20000 = -14000 + 20000 = 6000

Thus, according to the model, the car would be worth $6,000 after five years.

This algebraic calculation can be cross-verified with the graph if data points are visible. Typically, the graph should show a linear decline from $20,000 at year 0 to around $6,000 at year 5, aligning perfectly with the mathematical model. If the graph confirms this trend, then our algebraic projection matches the visual data accurately.

Understanding this relationship and the corresponding formula enhances predictive accuracy and supports better decision-making regarding asset management, resale timing, and financial planning.

References

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