An island has a carrying capacity of 1 million rabbits. (That is, no more than 1 million rabbits can be supported by the island.) The rabbit population is two at time t = 1 day and grows at a rate of r(t) thousand rabbits/ day until the carrying capacity is reached. For each of the following formulas for r(t), is the carrying capacity ever reached? Explain your answer.

(a) r(t) = 1∕t²

(b) r(t) = t

(c) r(t) = 1∕√t