Solve the problem.
-A thermometer reading 11°C is brought into a room with a constant temperature of 30°C. If the thermometer reads 17°C after 4 minutes, what will it read after being in the room for 7 minutes? Assume the cooling follows
Newton's Law of Cooling: $\mathrm { U } = \mathrm { T } + \left( \mathrm { U } _ { \mathrm { O } } - \mathrm { T } \right) \mathrm { e } ^ { \mathrm { kt } }$ (Round your answer to two decimal places.)
A) 28.67°C
B) 5.87°C
C) 20.22°C
D) 39.78°C

Question

Quizplus · Accepted Answer

Using Newton's Law of Cooling, we first find the constant $ k $ using the information given for 4 minutes. Then, we use this $ k $ to find the temperature at 7 minutes. The calculation shows that the temperature is approximately 20.22°C.

Solve the Problem U=T+(UO−T)ekt\mathrm { U } = \mathrm { T } + \left( \mathrm { U } _ { \mathrm { O } } - \mathrm { T } \right) \mathrm { e } ^ { \mathrm { kt } }U=T+(UO​−T)ekt

Solve the Problem $\mathrm { U } = \mathrm { T } + \left( \mathrm { U } _ { \mathrm { O } } - \mathrm { T } \right) \mathrm { e } ^ { \mathrm { kt } }$