Building a Function from Data

The data shown in Table 3 measure crop yield for various amounts of fertilizer:

1. Draw a scatter plot of the data and determine a possible type of relation that may exist between the two variables.
2. Use technology to find the function of best fit to these data.

Solution (a) Figure 37 on page 22 shows the scatter plot. The data suggest the graph of a quadratic function.

(b) The graphing calculator screen in Figure 38 shows that the quadratic function of best fit is \[ Y ( x) =-0.017x^{2}+1.0765x+3.8939 \] where \(x\) represents the amount of fertilizer used and \(Y\) represents crop yield. The graph of the quadratic model is illustrated in Figure 39.

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