From the previous question, we know that
T ( t ) − 19 = − 16 e k t {\displaystyle {\begin{aligned}T(t)-19=-16e^{kt}\end{aligned}}}
where
k = − ln ( 2 ) 30 {\displaystyle \displaystyle k={\frac {-\ln(2)}{30}}}
Searching for when T ( t ) = 16 {\displaystyle T(t)=16} yields
16 − 19 = − 16 e k t − 3 = − 16 e k t 3 16 = e k t ln ( 3 / 16 ) = k t ln ( 3 / 16 ) = − ln ( 2 ) t 30 t = − 30 ln ( 3 / 16 ) ln ( 2 ) t = 30 ln ( 16 / 3 ) ln ( 2 ) {\displaystyle {\begin{aligned}16-19&=-16e^{kt}\\-3&=-16e^{kt}\\{\frac {3}{16}}&=e^{kt}\\\ln(3/16)&=kt\\\ln(3/16)&={\frac {-\ln(2)t}{30}}\\t&=-30{\frac {\ln(3/16)}{\ln(2)}}\\t&=30{\frac {\ln(16/3)}{\ln(2)}}\end{aligned}}}
completing the question.
yields
