Example: If Robinson Crusoe fishes by hand, he can catch 20 fish each week. If he takes a week off to make a net, he can then catch 25 fish a week with the net until it wears out in 10 weeks. In order to avoid starving during the week that he is weaving the net, he can borrow 10 fish from Friday, on the condition that he pays back the 10 fish plus an extra 5 fish. The cost of the net is the 20 fish that he gave up by not fishing for a week plus the 5 extra fish paid to Friday, or 25 fish. The gross marginal productivity of the net (the total addition to productivity that it contributes) is (5 fish per week)•(10 weeks) = 50 fish. The net marginal productivity of the net (the total addition to productivity that it contributes, less its cost) is (50 fish) – (25 fish) = 25 fish.
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Fish • Most fish reproduce by laying eggs, though some fish, such as great white sharks, give birth to live babies called pups • Fish use a variety of low-pitched sounds to convey messages to each other. They moan, grunt, croak, boom, hiss, whistle, creak, shriek, and wail. They rattle their bones and gnash their teeth. However, fish do not have vocal chords. They use other parts of their bodies to make noises, such as vibrating muscles against their swim bladder • Saltwater fish need to drink more water than freshwater fish. Since seawater is saltier than the liquids in a fish’s body, water inside the fish is constantly flowing out. If they didn’t drink to replace the lost water, saltwater fish would dry up like prunes.
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Problem 34.17 A small tropical fish is at the center of a water-filled (n=1.33) spherical fishbowl 28cm in diameter. a) Find the apparent position and magnification of the fish to an observer outside the bowl. b) A friend advised the owner of the bowl to keep it out of direct sunlight to avoid blinding the fish, which might swim into the focal point of the parallel rays from the sun. Is the focal point actually within the bowl? For part a) consider the fish to be the light source, and calculate the image position for light rays exiting the bowl. Magnification can be found from this formula: m  na di nb do m  1. 33(  14cm) 1. 33 1(14cm) We will be using this formula: na nb nb  na   do di R Here is the given information: The fish appears larger by a factor of 1.33 na 1. 33; nb 1; do  14cm; R   14cm 1. 33 1 1  1. 33    di   14cm 14cm di  14cm This radius is negative because the center of the bowl is on the same side as the light source (the fish) A negative value for S’ means the image is on the same side of the interface as the object (i.e. inside the bowl in this case). So the observer will see a virtual image of the fish at the center of the bowl. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
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Rules in Detail: Fish Rules If the current cell contains a fish:  Fish live for 10 generations  If >=5 neighbors are sharks, fish dies (shark food)  If all 8 neighbors are fish, fish dies (overpopulation)  If a fish does not die, increment age 12
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29. Schooling Fish and Murres
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