The GATE Grind

GATE 2023 BM – Question 36

Engineering Mathematics · Differential Equations · 2 marks · Multiple choice

A bacterial population satisfies $dx/dt=x(1-x/200)$ with x(0)=100. What population is approached as t tends to infinity?

  1. 150
  2. 200
  3. 300
  4. 500

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) 200

Explanation

The logistic equation has equilibria zero and two hundred. Starting at one hundred, the derivative is positive until the carrying capacity two hundred is approached. Explicitly x(t)=200/(1+e⁻ᵗ), whose limiting value is two hundred. Therefore B.

More Differential Equations questions

All Differential Equations questions →