Newton's law of cooling indicates that the temperature of a warm object, such as a cake...

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Newton's law of cooling indicates that the temperature of a warm object, such as a cake coming out of the oven, will decrease exponentially with time and will 0 approach the temperature of the surrounding air. The temperature T (t) is modeled by T (t)=T+(TT)ekt. In this model, T represents the temperature of the surrounding air, To represents the initial temperature of the object, and t is the time (in minutes) after the object starts cooling. The value of k is a constant of proportion relating the temperature of the object to its rate of temperature change. a A cake comes out of the oven at 350F and is placed on a cooling rack in a 71F kitchen. After checking the temperature several minutes later inside the heater, the value of k is measured as 0.046. (a) Write a function that models the temperature T (t) (in F) of the cake t minutes after being removed from the oven. (b) What is the temperature of the cake 20 min after coming out of the oven? Round to the nearest degree. Do not round intermediate calculations. (c) It is recommended that the cake should not be frosted until it has cooled under 100F. If Jessica waits 1 hr to frost the cake, will the cake be cool enough to frost? Round to the nearest degree. Newton's law of cooling indicates that the temperature of a warm object, such as a cake coming out of the oven, will decrease exponentially with time and will 0 approach the temperature of the surrounding air. The temperature T (t) is modeled by T (t)=T+(TT)ekt. In this model, T represents the temperature of the surrounding air, To represents the initial temperature of the object, and t is the time (in minutes) after the object starts cooling. The value of k is a constant of proportion relating the temperature of the object to its rate of temperature change. a A cake comes out of the oven at 350F and is placed on a cooling rack in a 71F kitchen. After checking the temperature several minutes later inside the heater, the value of k is measured as 0.046. (a) Write a function that models the temperature T (t) (in F) of the cake t minutes after being removed from the oven. (b) What is the temperature of the cake 20 min after coming out of the oven? Round to the nearest degree. Do not round intermediate calculations. (c) It is recommended that the cake should not be frosted until it has cooled under 100F. If Jessica waits 1 hr to frost the cake, will the cake be cool enough to frost? Round to the nearest degree.

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a To model the temperature Tt of the cake in F we can use the equation Tt T To T ekt Given T 71F tem... View the full answer