T − t e m p e r a t r u r e T o u t − o u t s i d e d T d t = k ( T o u t − T ) , T ( t 0 ) = T 0 ⇒ T ( t ) = T o u t + ( T 0 − T o u t ) e − k ( t − t 0 ) = [ e − k = A ] = T o u t + ( T 0 − T o u t ) A t − t 0 T o u t = − 10 , t 0 = 0 , T 0 = 70 , T ( 2 ) = 26 ⇒ − 10 + ( 70 + 10 ) A 2 − 0 = 26 ⇒ A = 36 80 = 0.67082 A t t = 5 : T ( 5 ) = − 10 + 80 ⋅ A 5 − 0 = − 10 + 80 ⋅ 0.6708 2 5 = 0.867259 T o u t = 70 , t 0 = 5 , T 0 = 0.867259 ⇒ T ( 9 ) = 70 + ( 0.867259 − 70 ) ⋅ 0.6708 2 9 − 5 = 56.0007 T-temperatrure\\T_{out}-outside\\\frac{dT}{dt}=k\left( T_{out}-T \right) ,T\left( t_0 \right) =T_0\Rightarrow T\left( t \right) =T_{out}+\left( T_0-T_{out} \right) e^{-k\left( t-t_0 \right)}=\left[ e^{-k}=A \right] =T_{out}+\left( T_0-T_{out} \right) A^{t-t_0}\\\\T_{out}=-10, t_0=0,T_0=70,T\left( 2 \right) =26\Rightarrow -10+\left( 70+10 \right) A^{2-0}=26\Rightarrow A=\sqrt{\frac{36}{80}}=0.67082\\At\,\,t=5: T\left( 5 \right) =-10+80\cdot A^{5-0}=-10+80\cdot 0.67082^5=0.867259\\T_{out}=70,t_0=5,T_0=0.867259\Rightarrow T\left( 9 \right) =70+\left( 0.867259-70 \right) \cdot 0.67082^{9-5}=56.0007 T − t e m p er a t r u re T o u t − o u t s i d e d t d T = k ( T o u t − T ) , T ( t 0 ) = T 0 ⇒ T ( t ) = T o u t + ( T 0 − T o u t ) e − k ( t − t 0 ) = [ e − k = A ] = T o u t + ( T 0 − T o u t ) A t − t 0 T o u t = − 10 , t 0 = 0 , T 0 = 70 , T ( 2 ) = 26 ⇒ − 10 + ( 70 + 10 ) A 2 − 0 = 26 ⇒ A = 80 36 = 0.67082 A t t = 5 : T ( 5 ) = − 10 + 80 ⋅ A 5 − 0 = − 10 + 80 ⋅ 0.6708 2 5 = 0.867259 T o u t = 70 , t 0 = 5 , T 0 = 0.867259 ⇒ T ( 9 ) = 70 + ( 0.867259 − 70 ) ⋅ 0.6708 2 9 − 5 = 56.0007
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