英文导数数学题,求带过程赐教~!(第一问已解)Coroners estimate time of death using the rule of thumb that a body cools about 2 degrees F during the first hour after death and about 1 degree F for each additional hour. Assuming an air
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![英文导数数学题,求带过程赐教~!(第一问已解)Coroners estimate time of death using the rule of thumb that a body cools about 2 degrees F during the first hour after death and about 1 degree F for each additional hour. Assuming an air](/uploads/image/z/12568543-7-3.jpg?t=%E8%8B%B1%E6%96%87%E5%AF%BC%E6%95%B0%E6%95%B0%E5%AD%A6%E9%A2%98%2C%E6%B1%82%E5%B8%A6%E8%BF%87%E7%A8%8B%E8%B5%90%E6%95%99%7E%21%28%E7%AC%AC%E4%B8%80%E9%97%AE%E5%B7%B2%E8%A7%A3%EF%BC%89Coroners+estimate+time+of+death+using+the+rule+of+thumb+that+a+body+cools+about+2+degrees+F+during+the+first+hour+after+death+and+about+1+degree+F+for+each+additional+hour.+Assuming+an+air)
英文导数数学题,求带过程赐教~!(第一问已解)Coroners estimate time of death using the rule of thumb that a body cools about 2 degrees F during the first hour after death and about 1 degree F for each additional hour. Assuming an air
英文导数数学题,求带过程赐教~!(第一问已解)
Coroners estimate time of death using the rule of thumb that a body cools about 2 degrees F during the first hour after death and about 1 degree F for each additional hour. Assuming an air temperature of 68 degrees F and a living body temperature of 98.6 degrees F, the temperature T(t) in degrees F of a body at a time t hours since death is given by
T(t) = 68 + 30.6 e^{-kt}.
1. For what value of k will the body cool by 2 degrees F in the first hour?
k=0.06759
2. Using the value of k found above, after how many hours will the temperature of the body be decreasing at a rate of 1 degree F per hour?
after ?hours
3. Using the value of k found above, show by calculating both values that, 24 hours after death, the coroner's rule of thumb gives approximately the same temperature as the formula.
T(24)=? degrees F
rule of thumb gives T = ?degrees F
英文导数数学题,求带过程赐教~!(第一问已解)Coroners estimate time of death using the rule of thumb that a body cools about 2 degrees F during the first hour after death and about 1 degree F for each additional hour. Assuming an air
2.T(t) = 68 + 30.6 exp(-kt)
T'(t) = -30.6k exp(-kt)
-1 = -30.6 * 0.06759 * exp(-0.06759t)
t=10.8 (hour)
3.t=24 hour
T(24) = 68 + 30.6 exp(-0.06759 x 24) = 74.0 (F)
using the rule of thumb
T(24) = 98.6 - 2*1 - 1*(24-1) = 73.6 (F)