A bacterial population that obeys the discrete-time dynamical system bt+1 = rbt with the initial condition b0 has the solution bt = b0rt. For the following values of r and b0, state which populations increase to infinity and which decrease to 0. For those increasing to infinity, find the time when the population will reach 1010. For those decreasing to 0, find the time when the population will reach 103.
1. b0 = 108 and r = 1.1.
2. b0 = 108 and r = 1.5.
3. b0 = 108 and r = 0.5.
4. b0 = 108 and r = 0.9.