To solve this problem, we need to use the formula for exponential growth:
N = N0 * 3^t
where N is the final number of ants, N0 is the initial number of ants, 3 is the rate of growth (since the number of ants triples each week), and t is the number of weeks.
We are given that there are initially 200 ants, so N0 = 200. We want to find N at the end of 8 weeks, so t = 8. Substituting these values into the formula, we get:
N = 200 * 3^8
N = 200 * 6561
N = 1,312,200
Therefore, at the end of the eighth week, there will be 1,312,200 ants in the colony.