Home/Calculus II/Exponential growth and decay/Formula16.2. Exponential growth and decayFormulaIn 16.2. Exponential growth and decayFormulaCopy LaTeXdydt=ky⟹y(t)=y0ekt.\frac{dy}{dt}=ky \quad\Longrightarrow\quad y(t)=y_0e^{kt}.dtdy=ky⟹y(t)=y0ekt.Tagsantiderivativeecuaciones diferencialesequations differential growth and decay exponentialExplore the ideaExplore the ideaVariablestttParámetro o variable auxiliareeeBase of the natural logarithmConditions⟹\Longrightarrow⟹y(t)=y0ekt.y(t)=y_0e^{kt}.y(t)=y0ekt.Found an error? Contact us.Related formulasRelatedFormulaPn(x)=∑k=0nf(k)(a)k!(x−a)kP_n(x)=\sum_{k=0}^{n}\frac{f^{(k)}(a)}{k!}(x-a)^kPn(x)=k=0∑nk!f(k)(a)(x−a)kOpen formulaOpen in sectionRelatedHalf-life for k<0k<0k<0:t1/2=ln2∣k∣.t_{1/2}=\frac{\ln2}{|k|}.t1/2=∣k∣ln2.Open formulaOpen in section