Fields of Functions 1 Copyright © 2026 Pearson Education, Inc. Fields of Functions In global agriculture, scientists and farmers work to understand how crops grow under different conditions. Farmland varies worldwide due to climate, land features, and economic priorities. Some regions have advanced, specialized farming for specific crops or livestock. Others have large farms for exports and smaller farms focused on local food production. In regions with steady and reliable growing conditions, crops often grow at a consistent, predictable rate that fits a linear function. In variable conditions, growth may start slowly, accelerate rapidly, then level off or decline, aligning better with complex models such as quadratics. Recognizing the appropriate growth pattern enables farmers to optimize planting, irrigation, and productivity. During management of an international farming operation, two different crops are observed, each with distinct growth patterns over time. These functions model each crop’s yield in kilograms, f(t) and g(t), based on the number of weeks since planting, t. ● Crop A: f(t) = 1.8t + 2 ● Crop B: g(t) = –0.5t2 + 4t + 2 1. Evaluate f(t) for t = 0, 2, 4, 6, 8. a. f(0) = b. f(2) = c. f(4) = d. f(6) = e. f(8) = f. Use the values to describe how Crop A grows over time. What patterns do you notice? 2. Evaluate g(t) for t = 0, 2, 4, 6, 8. a. g(0) = b. g(2) = c. g(4) = d. g(6) = e. g(8) = f. Compare your answers with your partner. Are there any values where the crop yield starts to decrease? Explain your thinking.
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