Food Chains

7651 /www/nrich/html/content/id/7651/ 1 0000-00-00T00:00:00 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <ul id="stemLinks"> <li><a href="http://nrich.maths.org/8422">Warm-up</a></li> <li><a href="http://nrich.maths.org/7571">Try this next</a></li> <li><a href="http://nrich.maths.org/6163">Think higher</a></li> <li><a href="http://plus.maths.org/content/does-it-pay-be-nice-maths-altruism-part-i">Read: mathematics</a></li> <li><a href="http://en.wikipedia.org/wiki/Food_chain">Read: science</a></li> <li><a href="http://plus.maths.org/content/eat-drink-and-be-merry-0">Explore further</a></li> </ul> <div> </div> The following food chain exists in the African savanna. <mdo:image alt="" src="chain.jpeg" style="width: 640px; height: 857px;"></mdo:image> A tiger will eat 3 birds every day. These three birds will eat 10 caterpillars each, every day, totaling 30 caterpillars. The 30 caterpillars will eat one small bush together every day. a. The part of the savanna that these animals live in currently has 500 small bushes, calculate the amount of the other animals. b. As you go up the food chain, the amount of energy available to the following predator decreases. For this food chain, the amount of energy available decreases by 25% for every level in the chain. Calculate how much more energy the tiger could obtain from becoming a vegetarian and eating the bush rather than from eating birds. c. One year, a bacteria kills 5000 caterpillars. What effect will this have on the food chain? d. What would happen to the tiger, bird and caterpillar populations if the tigers decided to become vegetarians and eat bushes to keep alive instead of starving? </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">It is not envisaged that <a href="http://nrich.maths.org/7651">this problem</a> would be used as a class problem. It is more appropriate for an enthusiastic student or small group of students looking for a challenge to work on independently.</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> Fast solutions: a. 15000 caterpillars, 1500 birds 500 tigers. b. They are getting $\frac{42}{75}$ = 56 % of what could get. c. 10000 caterpillars = 1000 birds = 333 tigers, 267 tigers would starve. d. 89286 tigers Detailed solutions: a. The ratio is 1 bush : 30 caterpillars : 3 birds : 1 tiger, so with 500 bushes, 500 x 30 = 15000 caterpillars, 500 x 3 = 1500 birds, 500 x 1 = 500 tigers. b. Lets say one bush contains 100 energy points. Then the caterpillars eat it, and have 75 points available to them. The birds get 75% of these points, 56 points, so the tiger has 42 points available to it. From eating the bush it could have obtained 75 points, so it's obtaining 42/75 = 56 % of what it could get. c. We still have 500 bushes but now we have 10000 caterpillars, so 10000 x 10 = 1000 birds 10000/30 = 333 tigers The new numbers would be the equilibrium point, 267 tigers would starve. d. 500 bushes give 500 x 100 x 75 energy points. Tigers need 42 energy points, so the tiger population would increase to $\frac{500 \times 100 \times 75}{42}$ = 89286 tigers! The caterpillar and bird populations would be left with no food and would decrease unless they found another source of food. </mdoxml> 2 4 0 0 1 0 0 Food Chains Problem on food chains and the consequences of events in their habitat. Applications STEM - living world Applications Maths Supporting SET