Question

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

Answer 1

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