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Unformatted text preview: Math Learning Center Boise State 2010 Modeling with non-linear functions Business 8 Previously, we have discussed supply and demand curves. At that time we used linear functions. Linear models are often used when introducing concepts in other subjects due to the simplicity of linear graphs. But are real situations best modeled with linear graphs? Consider the supply curve. If we collect a few data points we might find a graph that looks like Looking closely at that graph we find that initially there is a large increase in price as we increase the quantity. However, at the larger quantities, increasing the quantity has less of an effect on the price. If we draw a curve through the points, we obtain the following: Looking at this graph, we should be able to recognize it as being similar to a square root graph. To make this easier to see, we will choose a scale that is easy to work with. P r i c e P r i c e Quantity Quantity Math Learning Center Boise State 2010 Consider the function g G u G U :. A few values of G have been given in the T-chart below. Compute the corresponding values for g G . Consider the above points with the points on the graph above and it is easy to determine that they are the same values (if this is not clear, re-compute your values in the chart.). Using a linear model for a demand curve we may have the function: g UU , and placing the supply and demand functions on the same graph, we have We now have a supply and demand equation and an equilibrium point somewhere between the quantity of 6 and 8....
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