Given dydt=−k(y−20)\frac{dy}{dt} = -k(y - 20)dtdy=−k(y−20) with y(0)=100y(0) = 100y(0)=100, what is the solution y(t)y(t)y(t)?
y(t)=20+80e−kty(t) = 20 + 80e^{-kt}y(t)=20+80e−kt
y(t)=100e−kt+20y(t) = 100e^{-kt} + 20y(t)=100e−kt+20
y(t)=80−20e−kty(t) = 80 - 20e^{-kt}y(t)=80−20e−kt
y(t)=100ekty(t) = 100e^{kt}y(t)=100ekt