The Celsius temperature of a hot potato placed in a room is given by the function T = 64* 2^{- .007 t} + 18 , 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 = 15.5 and t = 15.6 seconds seconds? 
• At what average rate is the temperature of the potato changing between clock times t = 15.5 and t = 15.51 seconds? 
• At what average rate is the temperature of the potato changing between clock times t = 15.5 and t = 15.501 seconds? 
• What do you estimate is the rate at which temperature is changing at clock time t = 15.5 seconds?

The rate at which the Celsius temperature of a hot potato placed in a room is given by Rate = .021 * 2^{- .007 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 = 15.5 and t = 31 seconds?