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when was the hobbit written - Parker Core Knowledge

📅 May 3, 2026 👤 scraface

May 03, 2026

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So capped at 100%.
However, in exponential growth models, sometimes unbounded, but capped...
But problem says improve by 12%, meaning multiplicative increase in ac...
But realistically, cannot exceed 100%.
Assuming the question wants the mathematical result without physical c...
× (1.12)^3 = 75 × 1.404928 = 105.3696.
So approximately 105.37%, but since can’t exceed 100, but question lik...
In math problems, often the formula is applied directly.
So: 75 × (1.12)^3 = 75 × 1.404928 = 105.3696.
But let's compute exactly:

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We are given the population model
\[ P(t) = P_0 e^{kt}, \]
and that the population triples in 5 hours, so
\[ P(5) = 3P_0. \]
Substitute into the equation:
\[ 3P_0 = P_0 e^{5k}. \]
Divide both sides by \( P_0 \):
\[ 3 = e^{5k}. \]
\[ \ln 3 = 5k. \]
Solve for \( k \):

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