1. Let P(t) represent the number, in hundreds, of bears in a population at time t years since 2000, when t 2 0. The population P(t) is increasing at a rate directly proportional to 8- P(t), where the constant of proportionality is k. (a) If P(0) = 5, find P(t) in terms of t and k. (b) If P(2) = 7, find k. (c) Find lim P(t). Interpret the meaning to this answer. t-+00