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Need help! please solve it with the series formula! (application of series) (2 Viewers)

thgus2114

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Joined
Oct 6, 2018
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8
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Male
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2019
Water evaporates from a pond at
an average rate of 7% each week.

(a) What percentage of water is
left in the pond after
(i) 1 week?
(ii) 2 weeks?
(iii) 3 weeks?
(b) What percentage is left after
15 weeks?
(c) If there was no rain,
approximately how long would
it take for the pond to only have
25% of its water left?
 

fan96

617 pages
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May 25, 2017
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NSW
Gender
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HSC
2018
Uni Grad
2024
Let denote the amount of water in the pond at the start of the week, expressed as a percentage of the original amount of water.

For geometric series we have



If the pond loses of its water each week, then that means that at the end of week there is of the water that was present at the start.

So we have .



Substitute to get the answers to a) and b).

(You need to add 1 because the amount of water after the first week is the amount of water at the start of the second week, etc.)

The easiest and quickest way to do c) is to simply check increasing values of .
 

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