Does the Drasilian Population Make Sense?

Assume the Yggdrasil started with a population of 40,000 people.

Part A

Does a population of 190,000 people make sense for the Yggdrasil after 178 years?  Justify your answer and discuss it in context of birth rates we have here on Earth.

List all your sources related to birth-rates and population growth equations.

Part B

The total journey for the Yggdrasil is estimated to be around 313 years long. Make an argument if you think this growth rate is sustainable for the duration of the journey, or will there need to be some pressure to reduce the population growth rate in the future? Don't forget to consider things like the available surface area per habitat ring and the fact that they are building a third habitat ring, Kepler III.

Rewards

Part A: +5 problem Solving; +5 Critical Thinking ; +5 Connections; +5 Research

Part B: Up to an additional +10 Problem Solving; +10 Critical Thinking; +10 Research