Home/Calculus II/Elementary differential equations/Exponential growth and decaySection 16.2Exponential growth and decayFormulavizCopy LaTeXdydt=ky⟹y(t)=y0ekt.\frac{dy}{dt}=ky \quad\Longrightarrow\quad y(t)=y_0e^{kt}.dtdy=ky⟹y(t)=y0ekt.⟹\Longrightarrow⟹y(t)=y0ekt.y(t)=y_0e^{kt}.y(t)=y0ekt.View detail →k>0k>0k>0: growth.k<0k<0k<0: decay.Half-life for k<0k<0k<0:Copy LaTeXt1/2=ln2∣k∣.t_{1/2}=\frac{\ln2}{|k|}.t1/2=∣k∣ln2.View detail →
FormulavizCopy LaTeXdydt=ky⟹y(t)=y0ekt.\frac{dy}{dt}=ky \quad\Longrightarrow\quad y(t)=y_0e^{kt}.dtdy=ky⟹y(t)=y0ekt.⟹\Longrightarrow⟹y(t)=y0ekt.y(t)=y_0e^{kt}.y(t)=y0ekt.View detail →