Differential Equations Newton's law of Cooling (Heating)

A cold beer initially at 35*F warms up to 40*F in 3 minutes while sitting in a room of temperature 70*F. How warm will the beer be if left out for 20 min?

I'm completely lost. I think it turns in to this

dT/dt = K[70-T]

and then becomes separable. I'm unsure about the above equation.

dT/dt = -k(T- Ta)
d (T(t)-Ta)/ dt = dy/dt =- k(T- Ta)= -ky
dy/dt = -ky
dy / y = -k dt
ln y(t) -ln y(0) = -kt
ln (y(t) / y(0)) = -kt
y(t) / y(0) =e^-kt
y(t) = y(0) e^-kt
substitute: y= T- Ta

T(t) - Ta = (T(0) -Ta) e^-kt
T(t) = (T(0) -Ta) e^-kt + Ta


T(t) = (T(0) -Ta) e^-kt + Ta
T(t)= Temperature of the beer at time t
T(0) = Initial Temperature of the beer = 35 deg F
Ta = Ambient temperature = 70 deg F
T(3) = 40

T(3)= 40 = (35-70) e^-k(3) + 70
k= 0.05138
T(20) = (35-70) e^-[0.05138(20)] + 70
T(20)= 57.48 deg F