The Celsius temperature of a hot potato placed in a room is given by the function T = 54* 2^{- .0038 t} + 23 , where t is clock time in seconds and T is temperature in Celsius.  

• At what average rate is the temperature of the potato changing between clock times t = 33 and t = 33.1 seconds seconds? 
• At what average rate is the temperature of the potato changing between clock times t = 33 and t = 33.01 seconds? 
• At what average rate is the temperature of the potato changing between clock times t = 33 and t = 33.001 seconds? 
• What do you estimate is the rate at which temperature is changing at clock time t = 33 seconds?

The rate at which the Celsius temperature of a hot potato placed in a room is given by Rate = .027 * 2^{- .0038 t}, where R is rate of change in Celsius degrees per second and t is clock time in seconds.  How much temperature change do you estimate would occur between t = 33 and t = 66 seconds?