Question
For a 60-day period, Amy observes how much of the lit side of the moon is visible each night. She starts her observations on a night when 0 percent of the lit side of the Moon is visible.
This is a line graph that represents how much of the Moon is visible to Amy each night of the 60-day period.
Predict the night when the next full moon will occur after Amy’s 60 days of observations. Explain your answer.
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This is a line graph that represents how much of the Moon is visible to Amy each night of the 60-day period.
Predict the night when the next full moon will occur after Amy’s 60 days of observations. Explain your answer.
Skip to input field
Answers
GPT-4o mini
To predict the night of the next full moon after Amy's 60 days of observations, we can analyze the lunar cycle. The lunar cycle, which includes the phases of the moon, is approximately 29.5 days long. This means that from one new moon to the next new moon, it takes about 29.5 days.
Since Amy starts her observations on a night when 0 percent of the lit side of the moon is visible, this corresponds to a new moon. Given that Amy observes for 60 days, we can calculate how many complete lunar cycles occur in that timeframe:
1. **Calculate how many lunar cycles fit into 60 days:**
\[
60 \div 29.5 \approx 2.03
\]
This means that there are about 2 complete lunar cycles in 60 days, with a remaining portion of approximately 1.05 days.
2. **Determine when the next full moon occurs:**
A full moon happens about halfway through the lunar cycle, approximately 14.75 days after the new moon. Thus, we can calculate the day of the first full moon and the second one:
- First full moon: Day 14.75 (around the end of the 15th day of observations)
- Second full moon: Another 29.5 days after the first full moon, which brings us to around Day 44.25 (approximately the end of the 44th day of observations).
Given that Amy's observations last for 60 days and considering the additional 1.05 days beyond 60 days, we can calculate when the third full moon would occur:
- Third full moon would be 29.5 days after the second full moon (Day 44.25):
\[
44.25 + 29.5 = 73.75
\]
Thus, the next full moon occurs approximately 73.75 days after the observed new moon, which translates to about 74 days after Amy's starting point. Since Amy observed for 60 days and then has to account for the additional days, the next full moon would occur around **the 15th day after she completes her observations on Day 60**, which is approximately **Day 15 after the 60 days**, putting it around **Day 74 of the overall timeline**.
In summary, if Amy's observations started from a new moon, the next full moon after her 60-day observation period would be around **Day 74**.
Since Amy starts her observations on a night when 0 percent of the lit side of the moon is visible, this corresponds to a new moon. Given that Amy observes for 60 days, we can calculate how many complete lunar cycles occur in that timeframe:
1. **Calculate how many lunar cycles fit into 60 days:**
\[
60 \div 29.5 \approx 2.03
\]
This means that there are about 2 complete lunar cycles in 60 days, with a remaining portion of approximately 1.05 days.
2. **Determine when the next full moon occurs:**
A full moon happens about halfway through the lunar cycle, approximately 14.75 days after the new moon. Thus, we can calculate the day of the first full moon and the second one:
- First full moon: Day 14.75 (around the end of the 15th day of observations)
- Second full moon: Another 29.5 days after the first full moon, which brings us to around Day 44.25 (approximately the end of the 44th day of observations).
Given that Amy's observations last for 60 days and considering the additional 1.05 days beyond 60 days, we can calculate when the third full moon would occur:
- Third full moon would be 29.5 days after the second full moon (Day 44.25):
\[
44.25 + 29.5 = 73.75
\]
Thus, the next full moon occurs approximately 73.75 days after the observed new moon, which translates to about 74 days after Amy's starting point. Since Amy observed for 60 days and then has to account for the additional days, the next full moon would occur around **the 15th day after she completes her observations on Day 60**, which is approximately **Day 15 after the 60 days**, putting it around **Day 74 of the overall timeline**.
In summary, if Amy's observations started from a new moon, the next full moon after her 60-day observation period would be around **Day 74**.