A cake recipe says to bake the cake until the center is 180 degrees, then let the cake cool to 120 degrees. Given a room temperature of 70 degrees,how long does it take the cake to cool to the desired temperature?
| Time (min) | Temp (F) |
| 0 | 180 |
| 5 | 126 |
| 10 | 94 |
| 15 | 80 |
| 20 | 73 |
+37163 Are you studying Newton's Law of Cooling? I THINK this is how to solve this Q:
T(t) = Ta + (Ti-Ta)e^-kt Ti = initial temp Ta = Temp ambient
T(t) = 126 = 70 + (180-70) e^-k5 results in k = .1350257
120 = 70+ (180-70)e^-(.1350257t) t = 5.84 minutes = 5 minutes 50 seconds
