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:
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,
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
So, the moon will be 100% illuminated between day 24 and day 25.
Learn more about expressions:
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