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

Multiple Choice

Solve the problem.
-Sandy manages a ceramics shop and uses a 650°F kiln to fire ceramic greenware. After turning off her kiln, she must wait until its temperature gauge reaches 205°F before opening it and removing the ceramic pieces. If room
Temperature is 70°F and the gauge reads 500°F in 8 minutes, how long must she wait before opening the kiln?
Assume the kiln cools according to 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 the nearest whole minute.)

A) 79 minutes
B) 56 minutes
C) 30 minutes
D) 39 minutes