50% illuminated: at day 12
100% illuminated: at day 24-25
Step-by-step explanation:
We know that:
- At day 1, the fraction of surface illuminated is 2%
- At day 2, the fraction of surface illuminated is 6%
...and so on
This means that the fraction of surface that is illuminated at day n is given by the expression:
[tex]f=2+4n[/tex]
where
n is the number of days
f is expressed as percentage
Here we want to find the day n at which the moon surface is 50% illuminated, so when
f = 50
Substituting into the expression and solving for n,
[tex]n=\frac{f-2}{4}=\frac{50-2}{4}=12[/tex]
So, the moon surface will be 50% illuminated at day 12.
Similarly, to find the day n at which the moon surface is 100% illuminated,
f = 100
So
[tex]n=\frac{f-2}{4}=\frac{100-2}{4}=24.5[/tex]
So, the moon will be 100% illuminated between day 24 and day 25.
Learn more about expressions:
brainly.com/question/7014769
brainly.com/question/11007572
brainly.com/question/11334714
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Answer:
Day 13= 50%
Day 26=100%
Step-by-step explanation:
Answers vary. Sample response: A simple approach is to attempt a linear model starting at Day 1. If the illumination is increased by 4% every day, then after 11 more days (after Day 2) it reaches 50%. In 13 more days, illumination reaches 100%. This gives a prediction of Day 13 for 50% and Day 26 for 100%.
