Homework for 16/19 December
Capture-Recapture Notes and Work
Big idea:
Example A (finding an unknown percent): In a capture-recapture process, 200 fish were tagged. From the recapture results, the game warden estimates that the lake contains 2500 fish. What percent of fish were tagged?
Solution: We know the ratio of tagged fish (the part) to total fish in the lake (the whole) is 200 to 2500. This ratio is equivalent to the percent p of tagged fish in the sample.
Write the proportion: (p/100)=(200/2500) and solve for p.
Example B (finding an unknown total): In a lake with 250 tagged fish, recapture results show that 11% of the fish are tagged. About how many fish are in the lake?
Solution: We can write 11% as the ratio , or 11 parts to 100 (the whole). The variable will be in the denominator, because the unknown quantity is the whole—the total number of fish in the lake.
Write the proportion: (11/100)=(250/f)
Invert both ratios: (100/11)=(f/250) and solve for f.
Example C (finding an unknown part): A lake is estimated to have 5000 fish after recapture experiments that showed that 3% of the fish were tagged. How many fish were originally tagged?
Solution: We can write 3% as the ratio , or 3 parts to 100 (the whole). The variable is in the numerator because the unknown quantity is the number of tagged fish (the part).
Write the proportion: (t/5000)=(3/100) and solve for t.
Questions:
1) In a capture-recapture process, 300 fish were tagged. From the recapture results, the game warden estimates that the lake contains 2800 fish. What percent of fish were tagged?
2) In a lake with 200 tagged fish, recapture results show that 16% of the fish are tagged. About how many fish are in the lake?
3) In a capture-recapture process, 150 fish were tagged. From the recapture results, the game warden estimates that the lake contains 2000 fish. What percent of fish were tagged?
4) A lake is estimated to have 7500 fish after recapture experiments that showed that 2% of the fish were tagged. How many fish were originally tagged?
5) In a lake with 150 tagged fish, recapture results show that 8% of the fish are tagged. About how many fish are in the lake?
6) A lake is estimated to have 3400 fish after recapture experiments that showed that 7.5% of the fish were tagged. How many fish were originally tagged?
7) The year after a dictionary was published, two librarians notified the publisher of mistakes. One librarian found 43 errors, and the other found 62. The reprint editor noticed that 35 of the errors were mentioned by both librarians. He used the capture-recapture method to estimate the actual number of errors. How many errors are there likely to be? (Hint: The errors found by either librarian can be used as the number of tagged errors in the capture phase. The other librarian represents the recapture phase, with the errors found by both being the tagged errors.)
8) When chemists write formulas for chemical compounds, they indicate how many atoms of each element combine to form a molecule of that compound. For instance, they write H2O for water, which means that there are two hydrogen atoms and one oxygen atom in each molecule of water. Acetone (or nail polish remover) has the formula C3H6O. The C stands for carbon.
a) How many of each atom are there in one molecule of acetone?
b) How many atoms of carbon must combine with 470 atoms of oxygen to form acetone molecules? How many atoms of hydrogen are required?
c) How many acetone molecules can be formed from 3000 atoms of carbon, 300 atoms of hydrogen, and 1000 atoms of oxygen?
9) Sulfuric acid is a highly corrosive substance used in the manufacture of dyes, fertilizer and medicine. Sulfuric acid is also used by artists for metal etching and in aqua tints. The molecular formula for sulfuric acid is H2SO4, where the S stands for the sulfur atom.
a) How many atoms of sulfur, hydrogen and oxygen are there in one sulfuric acid molecule?
b) How many atoms of sulfur would it take to combine with 200 atoms of hydrogen?
How many atoms of oxygen would it take to combine with 200 atoms of hydrogen?
c) If 500 atoms of sulfur, 400 atoms of hydrogen, and 400 atoms of oxygen were combined, how many sulfuric acid molecules could be formed?
Big idea:
Example A (finding an unknown percent): In a capture-recapture process, 200 fish were tagged. From the recapture results, the game warden estimates that the lake contains 2500 fish. What percent of fish were tagged?
Solution: We know the ratio of tagged fish (the part) to total fish in the lake (the whole) is 200 to 2500. This ratio is equivalent to the percent p of tagged fish in the sample.
Write the proportion: (p/100)=(200/2500) and solve for p.
Example B (finding an unknown total): In a lake with 250 tagged fish, recapture results show that 11% of the fish are tagged. About how many fish are in the lake?
Solution: We can write 11% as the ratio , or 11 parts to 100 (the whole). The variable will be in the denominator, because the unknown quantity is the whole—the total number of fish in the lake.
Write the proportion: (11/100)=(250/f)
Invert both ratios: (100/11)=(f/250) and solve for f.
Example C (finding an unknown part): A lake is estimated to have 5000 fish after recapture experiments that showed that 3% of the fish were tagged. How many fish were originally tagged?
Solution: We can write 3% as the ratio , or 3 parts to 100 (the whole). The variable is in the numerator because the unknown quantity is the number of tagged fish (the part).
Write the proportion: (t/5000)=(3/100) and solve for t.
Questions:
1) In a capture-recapture process, 300 fish were tagged. From the recapture results, the game warden estimates that the lake contains 2800 fish. What percent of fish were tagged?
2) In a lake with 200 tagged fish, recapture results show that 16% of the fish are tagged. About how many fish are in the lake?
3) In a capture-recapture process, 150 fish were tagged. From the recapture results, the game warden estimates that the lake contains 2000 fish. What percent of fish were tagged?
4) A lake is estimated to have 7500 fish after recapture experiments that showed that 2% of the fish were tagged. How many fish were originally tagged?
5) In a lake with 150 tagged fish, recapture results show that 8% of the fish are tagged. About how many fish are in the lake?
6) A lake is estimated to have 3400 fish after recapture experiments that showed that 7.5% of the fish were tagged. How many fish were originally tagged?
7) The year after a dictionary was published, two librarians notified the publisher of mistakes. One librarian found 43 errors, and the other found 62. The reprint editor noticed that 35 of the errors were mentioned by both librarians. He used the capture-recapture method to estimate the actual number of errors. How many errors are there likely to be? (Hint: The errors found by either librarian can be used as the number of tagged errors in the capture phase. The other librarian represents the recapture phase, with the errors found by both being the tagged errors.)
8) When chemists write formulas for chemical compounds, they indicate how many atoms of each element combine to form a molecule of that compound. For instance, they write H2O for water, which means that there are two hydrogen atoms and one oxygen atom in each molecule of water. Acetone (or nail polish remover) has the formula C3H6O. The C stands for carbon.
a) How many of each atom are there in one molecule of acetone?
b) How many atoms of carbon must combine with 470 atoms of oxygen to form acetone molecules? How many atoms of hydrogen are required?
c) How many acetone molecules can be formed from 3000 atoms of carbon, 300 atoms of hydrogen, and 1000 atoms of oxygen?
9) Sulfuric acid is a highly corrosive substance used in the manufacture of dyes, fertilizer and medicine. Sulfuric acid is also used by artists for metal etching and in aqua tints. The molecular formula for sulfuric acid is H2SO4, where the S stands for the sulfur atom.
a) How many atoms of sulfur, hydrogen and oxygen are there in one sulfuric acid molecule?
b) How many atoms of sulfur would it take to combine with 200 atoms of hydrogen?
How many atoms of oxygen would it take to combine with 200 atoms of hydrogen?
c) If 500 atoms of sulfur, 400 atoms of hydrogen, and 400 atoms of oxygen were combined, how many sulfuric acid molecules could be formed?
posted by e at 07:58
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