California produces nearly 95% of the processed tomatoes

Chapter 8, Problem 4

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California produces nearly 95% of the processed tomatoes grown in the United States, so managing irrigation water for tomatoes is a major issue. Agricultural researchers have been able to quantify the relationship between C, the canopy coverage, and KC, the crop coefficient.10 Canopy cover is the percentage of the total plot covered by shade produced by the leaves of the plants. The crop coefficient is a measure of the water needed by the plants. The following graph shows the relationship between the canopy coverage and the crop coefficient. a. As the plants grow, will the canopy cover increase or decrease? Why? b. As the canopy cover increases, the crop coefficient also increasesbut at a decreasing rate. Why would that be true? c. The best-fit function to the data is a quadratic: KC 0.126 (0.0172)C (0.0000776)C2 where 0 # C # 100%. i. The initial growth stage has between 0% and 10% canopy coverage. Estimate the corresponding crop coefficient for 10% canopy coverage from the graph, then calculate it using the quadratic model. ii. In the crop development growth stage, the canopy is between 10% and 75%. Estimate the crop coefficient when the canopy is at 75% and then calculate it. What does this number mean?