Answer
$$ 8th \ Day \\ 2700 \ mosquitoes$$
Work Step by Step
We assume that the insecticide is no longer effective when the number of mosquitoes killed is less than 1. Continuing the series for day 7:
$$ = \frac{7}{3} \\ =2.3$$
For the eight day:
$$ = .8 \ mosquitoes$$
It is ineffective after 8 days. The total mosquitoes killed is:
$$ =2096.4 + .8+2.3 \\ =2700 \ mosquitoes$$
