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

Answer: P = P₀ e^kt.

A P = P₀ + kt
B P = P₀ e^kt
C P = kt
D P = P₀/k

Correct answer: B. P = P₀ e^kt

Explanation: Separate: dP/P = k dt. Integrate: ln P = kt + C. P = P₀ e^kt. 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.

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Equations involving derivatives and their solutions

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

Concept context

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