Solve: T=Tf+T0e^-kt for t.

Question

Solve: T=Tf+T0e^-kt for t.

Answer 1

I assume Tf is supposed to be T_f, not T multiplied by f.

 

T = T_f + T₀e^-kt

 

(T - T_f)/T₀ = e^-kt

 

ln[(T - T_f)/T₀] = -kt

 

t = -(1/k) ln[(T - T_f)/T₀]

Answer 2

T=Tf+T₀e^-kt 

T(1-f)=T₀e^-kt

ln((T/T₀)(1-f))=-kt

t=(-1/k)ln((T/T₀)(1-f))