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

Question

Quizplus · Accepted Answer

Newton's Law of Cooling formula is $U = T + (U_0 - T)e^{kt}$, where $U$ is the temperature at time $t$, $U_0$ is the initial temperature, $T$ is the ambient temperature, and $k$ is a constant. Given $U_0 = 650°F$, $T = 70°F$, and $U = 500°F$ at $t = 8$ minutes, we first find $k$. Then, we solve for $t$ when $U = 205°F$. Following the steps to solve for $k$ and then for $t$ when $U = 205°F$, the calculation results in a time close to 39 minutes, rounded to the nearest whole minute.

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