21. Daylight in Fairbanks The viewing window below shows the number of hours of daylight in Fairbanks, Alaska, on each day for a typical 365-day period from January 1 to December 31. Answer the following questions by estimating slopes on the graph in hours per day. For the purposes of estimation, assume that each month has 30 days. [0, 365] by [0, 24] (a) On about what date is the amount of daylight increasing at the fastest rate? What is that rate? (b) Do there appear to be days on which the rate of change in the amount of daylight is zero? If so, which ones? (c) On what dates is the rate of change in the number of daylight hours positive? negative?
21. Daylight in Fairbanks The viewing window below shows the number of hours of daylight in Fairbanks, Alaska, on each day for a typical 365-day period from January 1 to December 31. Answer the following questions by estimating slopes on the graph in hours per day. For the purposes of estimation, assume that each month has 30 days. [0, 365] by [0, 24] (a) On about what date is the amount of daylight increasing at the fastest rate? What is that rate? (b) Do there appear to be days on which the rate of change in the amount of daylight is zero? If so, which ones? (c) On what dates is the rate of change in the number of daylight hours positive? negative?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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- **Graph Details:**
- The x-axis represents days of the year, ranging from 0 to 365.
- The y-axis represents the number of daylight hours, ranging from 0 to 24.
- The graph forms a sinusoidal curve, peaking in the middle of the year and dipping at the start and end of the year.
**Questions:**
(a) On about what date is the amount of daylight increasing at the fastest rate? What is that rate?
(b) Do there appear to be days on which the rate of change in the amount of daylight is zero? If so, which ones?
(c) On what dates is the rate of change in the number of daylight hours positive? Negative?
---
### Graph Explanation:
The graph demonstrates a typical pattern of daylight over a year in Fairbanks.
- **Peak Daylight:** Observed around mid-year, indicating the summer solstice when daylight is at its maximum.
- **Minimum Daylight:** Observed at both the beginning and end of the year, reflecting the winter solstice with minimum daylight.
### Rate of Change:
- **Fastest Increase:** Generally occurs during late winter to early spring, as the days begin to lengthen rapidly.
- **Zero Change (Plateaus):** Occurs at the solstices—around June and December when the increase or decrease in daylight levels off before reversing.
- **Positive Change:** From approximately January to June.
- **Negative Change:** From approximately July to December.
The graph is useful for understanding the cyclical pattern of daylight in high latitude regions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e635601-9da2-4fe2-987c-7194620410e8%2F40b55e61-4182-4ba4-8382-5d811811dab4%2F1lqfvf7_processed.png&w=3840&q=75)
Transcribed Image Text:**Daylight in Fairbanks**
The viewing window below shows the number of hours of daylight in Fairbanks, Alaska, on each day for a typical 365-day period from January 1 to December 31. Answer the following questions by estimating slopes on the graph in hours per day. For the purposes of estimation, assume that each month has 30 days.
- **Graph Details:**
- The x-axis represents days of the year, ranging from 0 to 365.
- The y-axis represents the number of daylight hours, ranging from 0 to 24.
- The graph forms a sinusoidal curve, peaking in the middle of the year and dipping at the start and end of the year.
**Questions:**
(a) On about what date is the amount of daylight increasing at the fastest rate? What is that rate?
(b) Do there appear to be days on which the rate of change in the amount of daylight is zero? If so, which ones?
(c) On what dates is the rate of change in the number of daylight hours positive? Negative?
---
### Graph Explanation:
The graph demonstrates a typical pattern of daylight over a year in Fairbanks.
- **Peak Daylight:** Observed around mid-year, indicating the summer solstice when daylight is at its maximum.
- **Minimum Daylight:** Observed at both the beginning and end of the year, reflecting the winter solstice with minimum daylight.
### Rate of Change:
- **Fastest Increase:** Generally occurs during late winter to early spring, as the days begin to lengthen rapidly.
- **Zero Change (Plateaus):** Occurs at the solstices—around June and December when the increase or decrease in daylight levels off before reversing.
- **Positive Change:** From approximately January to June.
- **Negative Change:** From approximately July to December.
The graph is useful for understanding the cyclical pattern of daylight in high latitude regions.
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