consider a water source that contains 60,000 gallons of water. Each day 9.4816 gallons of water are removed, but 95% of that water is returned on a daily basis. how long it take to run out fresh water, if water usage increase by 3% every year. write a function/equation

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consider a water source that contains 60,000 gallons of water. Each day 9.4816 gallons of water are removed, but 95% of that water is returned on a daily basis. how long it take to run out fresh water, if water usage increase by 3% every year. write a function/equation

Mathematics
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d0 = B d1 = B - a + ak d2 = (B - a + ak) -a +ak = B - 2a + 2ak d3 = B - 3a + 3ak ----------------- dn = B - na + nak dn = B +na(k-1) ---------------- 0 = B +na(k-1) -B = na(k-1) -B/(a(k-1)) = n
we are only losing 5% a day if 95% is returned dn = B -na(.05) 0 = B -na(.05) B = na(.05) B/a(.05) = n
but assuming we cant pull out a if there is less then a in there, we can work as: (B-a)/(a(.05)) now the questions is, should we allocate the 3% increase per year at the end of a year? or even it out over the course of the year?

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Other answers:

if we allocate it over a year, then a changes by (.03/365) each day dn = B +n(.05) a(1+.03/12)^(n-1) seems fair

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