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b) 20,000(1.06)^4t
If t = 4 years, then the population will be:
20,000(1.06)^4(4) = 20,000(1.06)^16 = 20,000(2.18) ≈ 43,600
Therefore, the population of the colony will be approximately 43,600 penguins 4 years after the start of the research study.