From $2003$ onward, the number of daily visitors to a website increased by $200\%$ every two years. so, for example, the number of visitors in $2011$ was $200\%$ more than the number of visitors in $2009$. in what year was the number of daily visitors $800\%$ more than the number of daily visitors in $2003$?

When we say an amount increased by some percentage, we usually mean that percentage is added to the original amount. In symbols, if there were V visitors in 2003, then in 2005 there were
  V + 200%×V = 3V
visitors. And in 2007 (after 2 more years), there were
  3(3V) = 9V
visitors. This represents an increase of
(9V -V)/V × 100% = 800%

The number of daily visitors in 2007 was 800% more than in 2003.