The data shown in Table 3 on page 22 measure crop yield for various amounts of fertilizer:
Solution (a) Figure 37 on page 22 shows the scatter plot. The data suggest the graph of a quadratic function.
Plot | Fertilizer, \(x\) (Pounds/\(100 \text{ft}^{2}\)) | Yield (Bushels) |
---|---|---|
1 | 0 | 4 |
2 | 0 | 6 |
3 | 5 | 10 |
4 | 5 | 7 |
5 | 10 | 12 |
6 | 10 | 10 |
7 | 15 | 15 |
8 | 15 | 17 |
9 | 20 | 18 |
10 | 20 | 21 |
11 | 25 | 20 |
12 | 25 | 21 |
13 | 30 | 21 |
14 | 30 | 22 |
15 | 35 | 21 |
16 | 35 | 20 |
17 | 40 | 19 |
18 | 40 | 19 |
(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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