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

Question

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

T=C+ (To-C) e ^kt

130=65+(195-65)e^30k

65=130e^30k

ln(65/130)=lne^30k

ln(.5)/30=-0.0231=k

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

T=65+130e^-0.0231t

replace t=35 to find your final answer