Chapter 1 | Functions and Graphs
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Table 1.6 Number of Units Sold n (in Thousands) as a Function of Price per Unit p (in Dollars)
In Figure 1.20 , we see the graph the number of units sold (in thousands) as a function of price (in dollars). We note from the shape of the graph that the number of units sold is likely a linear function of price per item, and the data can be closely approximated by the linear function n =−1.04 p +26 for 0≤ p ≤25, where n predicts the number of units sold in thousands. Using this linear function, the revenue (in thousands of dollars) can be estimated by the quadratic function R ( p ) = p · ⎛ ⎝ −1.04 p +26 ⎞ ⎠ =−1.04 p 2 +26 p for 0≤ p ≤25. In Example 1.15 , we use this quadratic function to predict the amount of revenue the company receives depending on the price the company charges per item. Note that we cannot conclude definitively the actual number of units sold for values of p , for which no data are collected. However, given the other data values and the graph shown, it seems reasonable that the number of units sold (in thousands) if the price charged is p dollars may be close to the values predicted by the linear function n =−1.04 p +26.
Figure 1.20 The data collected for the number of items sold as a function of price is roughly linear. We use the linear function n =−1.04 p +26 to estimate this function.
Example 1.15
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