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Answer :
T(t)= 205 F
T o = 220 F
T a = 72 F
t = 12 min;
Here: k ( constant ) = ?
205 = 72 + ( 220 - 72 ) * e ^( - 12 k )
133 = 148 * e ^(-12 k )
e^(-12k) = 0.89865
- 12 k = ln 0.86865
- 12 k = - 0.1068
k = 0.0089
Then we will plug in the formula:
175 = 72 + ( 220 - 72 ) * e^(-0.0089 t )
103 = 148 * e^(-0.0089 t )
e^(-0.0089 t ) = 0.6959
- 0.0089 t = ln 0.6959
- 0.0089 t = - 0.36255
t = 0.369255 : 0.0089
t = 40.73 ≈ 41 min
Answer: It will be 41 minutes later.
T o = 220 F
T a = 72 F
t = 12 min;
Here: k ( constant ) = ?
205 = 72 + ( 220 - 72 ) * e ^( - 12 k )
133 = 148 * e ^(-12 k )
e^(-12k) = 0.89865
- 12 k = ln 0.86865
- 12 k = - 0.1068
k = 0.0089
Then we will plug in the formula:
175 = 72 + ( 220 - 72 ) * e^(-0.0089 t )
103 = 148 * e^(-0.0089 t )
e^(-0.0089 t ) = 0.6959
- 0.0089 t = ln 0.6959
- 0.0089 t = - 0.36255
t = 0.369255 : 0.0089
t = 40.73 ≈ 41 min
Answer: It will be 41 minutes later.
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