course MTH 173
7/11/10 10:33 a.m.
The Celsius temperature of a hot potato placed in a room is given by the function T = 47* 2- .0033 t + 22 , 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 = 14.6 and t = 14.7 seconds seconds?
At what average rate is the temperature of the potato changing between clock times t = 14.6 and t = 14.61 seconds?
At what average rate is the temperature of the potato changing between clock times t = 14.6 and t = 14.601 seconds?
What do you estimate is the rate at which temperature is changing at clock time t = 14.6 seconds?
The rate at which the Celsius temperature of a hot potato placed in a room is given by Rate = .045 * 2- .0033 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 = 14.6 and t = 29.2 seconds?
t T
14.6 67.4563
14.601 67.4562
14.61 67.4553
14.7 67.4459
avg rate of change between clock times 14.6 and 14.7 = (67.4459-67.4563)/(14.7-14.6)= -.104 deg C/sec
avg rate of change between clock times 14.6 and 14.61 = (67.4553-67.4563)/(14.61-14.6)= -.1 deg c/sec
avg rate of change between clock times 14.6 and 14.601= (67.4562-67.4563)/(14.601-14.6)= -.1 deg c/sec
to get a useful number of significant figures in the difference, your quantities have to be calculated to a sufficient number of significant figures. For that last calculation depths would need to be carried out to 8 or more significant figures, in order to get at least 3 in the difference.
I estimate the rate of temp changing at clock time 14.6 seconds to be -.103976 degc/sec
R=.045*2^-.0033t
t=14.6
t=29.2
R(14.6)=.045 * 2^-.0033(14.6)=.043522
R(29.2)=.045 *2^-.0033(29.2)=.042093
(.043522+.042093)/2=.042808 degc/sec
(29.2-14.6)*.042802= .624982 change in temp from 14.6 to 29.2 "
Very good, but be sure to see my note on significant figures.
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