Which statements about $x(t) = x_0 e^{rt}$ are true?

• B. Continuous compounding at rate $r$ yields more than simple annual $r$
• C. It solves $\dot{x} = rx$ for any initial value $x_0$
• D. With $r < 0$ it decays toward zero without ever crossing it

Doubling time $\ln 2/r$ is the exponential’s magic: independent of size. A million doubles as fast as a hundred, which is why compounding stories end so dramatically.