A population of bacteria is increasing at a rate of 1000 / (2 + 3t)0.75 bacteria per hour, starting from a population of 106. Could this sort of growth be maintained indefinitely? When would the population reach 2.0 × 106? Would you say that this population is growing quickly?
Write pure-time differential equations to describe the above situations, find out what happens over the long term, and state whether the rule could be followed indefinitely.