Question

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

Answer 1

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

Answer 2

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

Answer 3

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?

Answer 4

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