Eksponentiell vekst
Ein ny type differentiallikning
September 2016
$$\frac{dy}{dt} = \frac{y}{2}$$
$$\frac{d}{dt} e^{\frac{t}{2}} = \frac{1}{2}e^{\frac{t}{2}}$$
$$y = e^{\frac{t}{2}}$$
$$y'(t) = k\cdot y$$
$$\frac{d}{dt} e^{kt} = k e^{kt}$$
$$\frac{d}{dt} C\cdot e^{kt} = k \cdot C\cdot e^{kt}$$
$$y(0) = C\cdot e^{kt}|_{t=0} = C$$