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📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 t > \frac{2.9957}{0.3} \approx 9.9857

📌 The smallest integer greater than 9.9857 is \(t = 10\).

📌 \[ P(9) = 2e^{2.7} \approx 2 \times 14.88 = 29.76 < 40 \]

📌 \[ P(10) = 2e^{3} \approx 2 \times 20.0855 = 40.171 > 40 \]

📌 So, the population first exceeds 40 after \(\boxed{10}\) full days.

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Now take derivative:
P'(x) = -\frac{5000}{x^2} + 0.5
-\frac{5000}{x^2} + 0.5 = 0 \Rightarrow \frac{5000}{x^2} = 0.5 \Righta...
Since \( x > 0 \), \( x = 100 \).
Second derivative: \( P''(x) = \frac{10000}{x^3} > 0 \) for \( x > 0 \...
Thus, production level 100 units minimizes average cost.
Even though original function has \( -0.5x^2 \), which breaks realism,...
Given the instruction to generate similar difficulty, we proceed with...
So, revise: The cost function is \( C(x) = 5000
Astor Bennett’s Shocking Secret Would Shock Every Fan—You Won’t Believ...

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But in the format, they use <<>> for computation, then #### with numbe...
But prior examples have exact integers.
Perhaps the 25% is meant to be 25 percentage points? But that would be...
Or perhaps increases by 25 in number, but no, it says 25%.
Another idea: perhaps rate means people per hour, and increase is mult...
But to resolve, use the exact value and round to nearest whole number...
Looking back at user instruction: output only the questions and soluti...
So to ensure integer, perhaps adjust the total. But we must use the sc...
But in math competitions, non-integer answers are rare for countable i...
So perhaps rephrase the problem to ensure integer.

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