# The level of a chemical pollution in a lake is 4.50 ppb and if the level increases by 0.20 ppb in the following month and by 5.0% less each month thereafter, what will be the maximum level

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by sweetysiri92

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by sweetysiri92

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Month1 : pollution increases by 0.20 ppb parts per billion (10^-9)

month 2 : increases by 0.20 * 0.95 as 0.95= (100-5)/100

month 3 : 0.20 * 0.95 * 0.95

So it is a geometric series : A = 0.20 R = 0.95

Sum to infinite terms is = A / (1 - 0.95) series converges as R < 1

So increase in pollution level = 0.20 / 0.05 = 4 ppb

*Maximum pollution level : 4.5 ppb + 4 ppb = 8.5 ppb*

month 2 : increases by 0.20 * 0.95 as 0.95= (100-5)/100

month 3 : 0.20 * 0.95 * 0.95

So it is a geometric series : A = 0.20 R = 0.95

Sum to infinite terms is = A / (1 - 0.95) series converges as R < 1

So increase in pollution level = 0.20 / 0.05 = 4 ppb