\(\boxed{b = -5, \, c = 6}\)
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- Thus, the values of \( b \) and \( c \) in terms of the ratio are:
- \[ b = -5k, \quad c = 6k^2 \]
- Given the ratio, if \( b = -5 \), then \( k = 1 \) and \( c = 6 \). Therefore, the specific values solving the problem are:
- An oceanographer studying the impacts of climate change is modeling the growth of algae blooms in a coastal region. The growth rate \( G(t) \) of the algae over time \( t \) is modeled by the function:
- \[ G(t) = \frac{3t^2 + 2t + 1}{t + 1} \]
- Find the horizontal asymptote of this function as \( t \to \infty \).
