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
来源：学生作业帮助网 编辑：六六作业网 时间：2024/12/25 14:48:02
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)