on the first day after the new moon 2% of the moons surface is illuminated. on the second day, 6% is illumina

Question

3 years ago

12

ted. based on this information, predict the day on which the moons surface is 50% illuminated and 100% illuminated.

1 answer:

Amanda [17] · Answer 1 · 2022-06-26T18:22:13+03:00

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:

$f=2+4n$

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,

$n=\frac{f-2}{4}=\frac{50-2}{4}=12$

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

$n=\frac{f-2}{4}=\frac{100-2}{4}=24.5$

So, the moon will be 100% illuminated between day 24 and day 25.

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on ﻿the ﻿first ﻿day ﻿after ﻿the ﻿new ﻿moon ﻿2% of ﻿the ﻿moons ﻿surface ﻿is ﻿illuminated. ﻿on ﻿the ﻿second ﻿day, 6% ﻿is ﻿illumina