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\boxed{a = 1, \, b = 2, \, c = 3}
Question:** A zoologist observes that the population \( P(t) \) of a certain species in the Amazon rainforest follows the quadratic model \( P(t) = kt^2 + mt + n \). Given \( P(1) = 120 \), \( P(2) = 150 \), and \( P(3) = 210 \), find the coefficients \( k \), \( m \), and \( n \).
\( P(1) = k(1)^2 + m(1) + n = 120 \implies k + m + n = 120 \)

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