This is a question about exponential growth. If N(t) is the number of bacteria after time t, then , where r is the rate at which the bacteria doubles with respect to t, so in hours. In this problem, it doubles every 3.5 hours, so when t=3.5 we want "rt"=1. That's so we get . So to make this expression work, we need rt=1, when t=3.5, so r=(1/3.5). Let's assume that the initial population of bacteria was 1, so our final equation is:

Now what you need to do is set this equation equal to 864 and solve for t, do the same for 442368, then calculate the difference in the t's.