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Social animals that live in groups can spend less time scanning for predators than solitary...

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Calculus

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Social animals that live in groups can spend less time scanning for predators than solitary individuals However they waste time fighting with the other group members over the available food There is some group size at which the net benefit is greatest because the animals spend least time on these unproductive activities and thus can spend time on feeding mating etc Assume that for a group of size x the fraction of time spent scanning for predators is 1 x 1 and the fraction of time spent fighting with other animals over food is F x B x 1 S x A where A B are constants and A 2B Find the size of the group for which the time wasted on scanning plus time wasted on fighting is smallest

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