📝 Logistic Curves

📖 From Calculus • 5. The derivative in graphing and applications • 24 questions available

Practice MCQs for Logistic Curves. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-15

Easy Questions

Medium Questions

Hard Questions

Q1. Which of the following formulas correctly represents a standard logistic function?

🔹 A. \(L(x)=Ke^{-bx}\)

🔹 B. \(L(x)=\frac{K}{1+Ae^{-bx}}\)

🔹 C. \(L(x)=K\ln(1+Ax)\)

🔹 D. \(L(x)=\frac{K}{1-Ae^{-bx}}\)

💡 Difficulty: easy | ✅ Correct: C

Q2. A population follows the logistic model \(P(t)=\frac{500}{1+4e^{-0.3t}}\). What is the carrying capacity and the initial population at \(t=0\)?

🔹 A. \(K=500,\;P(0)=100\)

🔹 B. \(K=500,\;P(0)=125\)

🔹 C. \(K=4,\;P(0)=500\)

🔹 D. \(K=500,\;P(0)=250\)

💡 Difficulty: medium | ✅ Correct: D

Q3. Solve for \(x\) when the logistic function \(L(x)=\frac{100}{1+4e^{-0.5x}}\) equals half its carrying capacity.

🔹 A. \(x=\frac{\ln 4}{0.5}\)

🔹 B. \(x=-\frac{\ln 4}{0.5}\)

🔹 C. \(x=0\)

🔹 D. \(x=\frac{\ln 2}{0.5}\)

💡 Difficulty: hard | ✅ Correct: C

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