My calculus class just began a new unit on differential equations and my teacher assigned a problem for extra credit. It's a word problem involving Newton's Law of Cooling. We only went through one quick example problem in class so I'm unsure of how to proceed on this. Any help is greatly appreciated.
A cake comes out of a 350-degree oven and is set aside to cool in a 70-degree kitchen. If 10 minutes after removal from the oven, the temperature of the cake is 280 degrees, how long after the cake was removed from the oven will it be safe to frost the cake, given the frosting process requires that the cake be no hotter than 100 degrees?