MATH 102 Lecture Notes - Lecture 18: Situation Two
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Lecture 18 - optimal foraging: the energy gained from t minutes at a patch is given by: , where e and k are positive constants. Over time, they tired, and eating honey got easier and easier. (yeager, chapter 7 slide 7: collecting food was going great, until the birds showed up and started stealing away my stash. (yeager, chapter 7 slide 7) Situation 1: bird"s stealing speed < me collecting speed. Situation 2: bird"s stealing speed >me collecting speed. Goal: to optimize the efficiency of energy consumption where is the time needed to travel to a patch: find t that make r(t) become maximum which is the optimal time in a single patch. Step 1: approximate the graph using x near 0 and x is far from 0. Step 2: find the critical point by setting r"(t) = 0. , it is the optimal residence time in 1 patch.
