Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 4 - Graphs of the Circular Functions - Section 4.1 Graphs of the Sine and Cosine Functions - 4.1 Exercises - Page 147: 58b

Answer

A large amplitude of oscillations reflects large changes in the levels of carbon dioxide in the atmosphere. Since Hawaii is generally warm year-round, there would not be very large differences in the growth of plants during the year. Therefore, we would expect the amplitude of oscillations to be quite small in Hawaii's graph. However, Barrow, Alaska, is located much farther north than Hawaii. There would be significant differences in plant growth in different seasons. During the cold winter months, there would be virtually no plant growth and thus no photosynthesis, while in warmer summer months, there would be significant plant growth. Therefore, we would expect to see larger differences in carbon dioxide levels in different seasons. The large amplitude of oscillations in Barrow's graph reflect the large differences in carbon dioxide levels in different seasons.

Work Step by Step

During the year, the amplitude of oscillations reflects the seasonal increase and decrease of carbon dioxide levels. During the spring and summer, plants absorb large amounts of carbon dioxide from the atmosphere due to photosynthesis. This results in a decrease in the carbon dioxide level in the atmosphere during the spring and summer. As there is little or no photosynthesis activity during the fall and the winter, there is an increase in the level of carbon dioxide in the atmosphere during fall and winter. A large amplitude of oscillations reflects large changes in the levels of carbon dioxide in the atmosphere. Since Hawaii is generally warm year-round, there would not be very large differences in the growth of plants during the year. Therefore, we would expect the amplitude of oscillations to be quite small in Hawaii's graph. However, Barrow, Alaska, is located much farther north than Hawaii. There would be significant differences in plant growth in different seasons. During the cold winter months, there would be virtually no plant growth and thus no photosynthesis, while in warmer summer months, there would be significant plant growth. Therefore, we would expect to see larger differences in carbon dioxide levels in different seasons. The large amplitude of oscillations in Barrow's graph reflect the large differences in carbon dioxide levels in different seasons.
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