What is the temperature of the cake after 35 minutes?

Question

- kt Over a period of time, a hot object cools to the temperature of the surrounding air. This is described mathematically by Newton's Law of Cooling T=C+ (To-C) e where t is the time it takes for an object to cool from temperature To to temperature T, C is the surrounding air temperature, and k is a positive constant that is associated with the cooling object. A cake removed from the oven has a temperature of 195°F and is left to cool in a room that has a temperature of 65°F. After 30 minutes, the temperature of the cake is 130°F.

What is the temperature in Fahrenheit of the cake after 35 minutes?

Answer 1

Typically, the equation is written as (T-T_Amb)/(T₀-T_Amb) = e^-kt where the LHS goes from 1 at t = 0 to 0 as t goes to infinity. T_amb is T of ambient environment.

1) Use 30 minute data to solve for k = -(1/t) ln((T-T_Amb)/(T₀-T_Amb)) k will be in inverse minutes. You can stay in Fahenheit, because the temperatures are differences.

2) Use 35 minute daya to solve for T = T_Amb + (T₀-T_Amb)e^-kt

Please consider a tutor. Take care.

Sorry I had screwed up the subscripts.