A population of rodents has a birth rate proportional to the population and a death rate proportional to the square of the population. The rate of change of the population is the difference between the birth and death rates. If the population starts with 20 rodents and is increasing at a rate of 2.4 rodents per month when there are 60 rodents, and at a rate of 2.1 rodents per month when there are 70 rodents, how long will it take for the population to grow to 90 rodents? What is the limiting number?

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