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The Celsius temperature of a hot potato placed in a room is given by the function T = 40* 2- .007 t + 24 , 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 = 6.8 and t = 6.9 seconds seconds?
At what average rate is the temperature of the potato changing between clock times t = 6.8 and t = 6.81 seconds?
At what average rate is the temperature of the potato changing between clock times t = 6.8 and t = 6.801 seconds?
What do you estimate is the rate at which temperature is changing at clock time t = 6.8 seconds?
The rate at which the Celsius temperature of a hot potato placed in a room is given by Rate = .041 * 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 = 6.8 and t = 13.6 seconds?
T = 40 * 2^(-.007(6.8)) + 24 = 62.7018
T = 40 * 2^(-.007(6.9)) + 24 = 62.683
Average rate of temp change between 6.8 and 6.9 is 0.188
T = 40 * 2^(-.007(6.8)) + 24 = 62.7018
T = 40 * 2^(-.007(6.81)) +24 = 62.6999
Average rate of temp change between 6.8 and 6.81 is 0.19
T = 40 * 2^(-.007(6.8)) + 24 = 62.7018
T = 40 * 2^(-.007(6.801)) + 24 = 62.7016
Average rate of temp change between 6.8 and 6.801 is 0.2057
Estimated rate of temp change at 6.8 is - .201
R = .041 * 2^-.007(6.8) = .03967
R = .041 * 2^-.007(13.6) = .03838
The average rate is .039025, multiplied by the difference in time (6.8), is .26537
A temp change between 6.8 and 13.6 is - .26537 degrees C (negative because the potato is cooling down).
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