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Home » 8 Mind-Blowing Many Toon Clips That Are Going Viral – Can You Guess #7? - 500apps

8 Mind-Blowing Many Toon Clips That Are Going Viral – Can You Guess #7? - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 As \( t \to \infty \), the term \( e^{-0.1(t-5)} \to 0 \). Thus, the denominator approaches 1:

📌 \[ P \to \frac{500}{1 + 0} = 500 \]

📌 Therefore, the population approaches \(\boxed{500}\) as \( t \to \infty \).

📌 A health data analyst models patient recovery rates with the function \( R(x) = \ln(x^2 + 4x + 5) \). Find the value of \( x \) that maximizes \( R(x) \).

📌 To maximize \( R(x) = \ln(x^2 + 4x + 5) \), we first find the derivative \( R'(x) \) and set it to zero.

📌 Differentiate \( R(x) \):

📌 \[ R'(x) = \frac{d}{dx}[\ln(x^2 + 4x + 5)] = \frac{2x + 4}{x^2 + 4x + 5} \]

📌 Set the derivative to zero:

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5p + q = 35 \quad \text{(Equation 5)}
2p = 10
p = 5
Substitute \( p = 5 \) back into Equation 4:
3(5) + q = 25
+ q = 25
q = 10
Substitute \( p = 5 \) and \( q = 10 \) back into Equation 1:
+ 10 + r = 15
+ r = 15

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