Multiple choice

Biotransformation of an organic compound having concentration (x) can be modelled using an ordinary differential equation $\frac{dx}{dt} + kx^2 = 0$, where k is the reaction rate constant. If x = a at t = 0, then the solution of the equation is

  1. x = ae-kt
  2. $\frac{1}{x} = \frac{1}{a} + kt$

  3. x = a (1 - e-kt)

  4. x = a + kt
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

dx/dt = -kx^2. Separating variables: dx/x^2 = -k*dt. Integrating both sides: -1/x = -kt + C. At t=0, x=a, so -1/a = C. Thus, -1/x = -kt - 1/a, which simplifies to 1/x = 1/a + kt.

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