x | 0 | 2 | 4 | 6 | 8 | y | 80000 | 60000 | 40000 | 20000 | 0 |
From the graph we see that the model shows that the car would have a value of zero after 8 years. This is almost certainly wrong. The model further shows that after 8 years the value would become negative, which would certainly not be true. We would not expect a linear model to be appropriate for all values of time in this situation.
Linear models are the simplest models, which can be too simplistic for some situations. Often a model may not represent real life scenarios. However, it can still be useful to us even if it is not perfect. Using a model can be better than just guessing what will happen. Even if the situation cannot be modeled with a linear equation for all values of the variables, the model might be very good for some of the values.
An improved model could well represent the depreciation in the value of a car and the corresponding the graph could look like the following:Part of the relationship might be linear, or approximately linear, and part might be non-linear. The mathematical form of the model displayed here would be more complicated than a linear equation.
Exercise 3: Two salespeople work for the same company. Their monthly incomes are calculated as follows.Questions: Draw an accurate graph of these equations for x = 0 to x = 80000 on the same diagram, using the horizontal axis for x and the vertical axis for y.
Solution:x | 0 | 4000 | 80000 | y | 5000 | 6200 | 7400 |
x | 0 | 2 | 4 | 6 | 8 | y | 80000 | 60000 | 40000 | 20000 | 0 |