# Need help! please solve it with the series formula! (application of series) (1 Viewer)

#### thgus2114

##### New Member
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
Let $\bg_white T_n$ denote the amount of water in the pond at the start of the $\bg_white n^{\rm th}$ week, expressed as a percentage of the original amount of water.

For geometric series we have

$\bg_white T_n = ar^{n-1}$

If the pond loses $\bg_white 7\%$ of its water each week, then that means that at the end of week there is $\bg_white 93\%$ of the water that was present at the start.

So we have $\bg_white a =1, \, r = 0.93$.

$\bg_white T_n = \left(0.93\right)^{n-1}$

Substitute $\bg_white n = 2, \, 3, \, 4,\, 16$ 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 $\bg_white n$.