📐 Mathematics · Differential Equations · JEE

For exponential growth model: dP/dt = kP (k > 0), the solution is:

Answer: P = P₀ e kt.

A P = P₀ + kt
B P = P₀ ekt
C P = kt
D P = P₀/k

Correct answer: B. P = P₀ ekt

Explanation: Separate: dP/P = k dt. Integrate: ln P = kt + C. P = P₀ ekt. Classic exponential growth.

The general solution y=Ax² represents an entire FAMILY of curves, one for each value of the arbitrary constant A; a particular solution (fixed by an initial condition) selects exactly one curve from this family.

Concept context

Equations involving derivatives and their solutions

Read the full Differential Equations notes →

For exponential growth model: dP/dt = kP (k > 0), the solution is:

Concept context

More Differential Equations questions