A population of bacteria is increasing at a rate of 1000 / (2 + 3t)1.5 bacteria per

Question:

A population of bacteria is increasing at a rate of 1000 / (2 + 3t)1.5 bacteria per hour, starting from a population of 1000. Could this sort of growth be maintained indefinitely? Would the population reach 2000?
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.