y = 78 + 0.6 \cdot \frac{5}{6} \cdot (90 - 84)

February 22, 2026

$y = 78 + 0.6 \cdot \frac{5}{6} \cdot (90 - 84)$

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$ x = 90 $
The regression line of $ y $ on $ x $ is:
y = \mu_y + r \cdot \frac{\sigma_y}{\sigma_x} (x - \mu_x)
y = 78 + 0.6 \cdot \frac{5}{6} \cdot 6 = 78 + 0.6 \cdot 5 = 78 + 3 = 81
The predicted technical score is $\boxed{81}$.
Question: In a biotechnology experiment, a bacterial culture grows such that the population $ P(t) $ after $ t $ hours is modeled by $ P(t) = P_0 \cdot e^{kt} $. If the population triples every 5 hours, how long will it take to grow from 200 to 16200 bacteria?

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