Consider the equation dydt=−7y\frac{dy}{dt} = -7ydtdy=−7y. If y(0)=10y(0) = 10y(0)=10, what is the value of y(t)y(t)y(t)?
y(t)=10−7ty(t) = 10 - 7ty(t)=10−7t
y(t)=7e−10ty(t) = 7e^{-10t}y(t)=7e−10t
y(t)=10e7ty(t) = 10e^{7t}y(t)=10e7t
y(t)=10e−7ty(t) = 10e^{-7t}y(t)=10e−7t