An invasive bacterial population doubles in the bloodstream of the invaded organism every 3.0 hours after entry. If the total number of bacteria in the bloodstream reaches 106 before suitable antibiotics are administered, the invaded organism will die. If 100 live bacteria make it into the bloodstream through a cut, how many hours, correct to the nearest whole hour, does it take before the bacterial population reaches a lethal level?
I thought this problem should have been pretty easy, everytime I do it my answer comes up around 50, but the real answer is 40. Can anyone show me how to do this problem correctly?