What is a solution to the differential equation #dT+k(T-70)dt# with T=140 when t=0?

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Answer 1 · 2016-07-18T19:03:45

#T(t) = 70 (1 + e^(-kt) )#

#dT+k(T-70)dt color{red}{= 0}# Ahem, that was missing

this is separable

#(dT)/(dt)= - k(T-70)#

#1/(T-70) (dT)/(dt)= - k#

#int \ 1/(T-70) (dT)/(dt) \ dt = - k int \ dt#

#int \ 1/(T-70) dT = - k int \ dt#

#ln (T-70) = - kt + C#

#T-70 = e^ (- kt + C) = C e^(-kt)#

Applying IV

#140-70 = C e^(-k(0)) implies C = 70#

#T(t) = 70 (1 + e^(-kt) )#