The law of uninhibited growth is express as:
where N(t) is the population at time t, N0 is the initial population, k is the growth rate and t is the time. In this case we know that after one day, t=1, the population is 800 and that the initial population was 500; plugging these values and solving for k we have:
Now that we have the growth rate, we know that the population growth in this case can be express as:
We want to know the time it takes for the population to be 7000, to find it we equate our expression to this value and solve for t:
Therefore, it takes 5.6 days for the population to reach 7000 individuals.