Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between the temperature of the object, T, and the ambient (environmental) temperature, E. This leads to the differential equation

dTdt=k(E−T)

where k>0 is a constant that represents the material properties and, E is the ambient temperature. (We will assume that E is also constant.)

The function

T(t)=E+(T0−E)e−kt

represents the temperature at time t that satisfies the differential equation.

The time of death of a murder victim can be estimated from the temperature of the body if it is discovered early enough after the crime has occurred. Suppose that in a room whose ambient temperature is E=17 degrees C, the temperature of the body upon discovery is T=28 degrees, and that a second measurement, one hour later is T=22.5 degrees. How many minutes before the body was discovered did the murder occur? (You should use the fact that just prior to death, the temperature of the victim was 37 degrees Celcius.)



진짜 죄송한데 이거 풀어주실분 계시나요?

이문제만 잡고 다섯시간짼데 도저히 풀리지 않습니다 제발 도와주세요..


말토즈 님 정말 감사합니다 ^_^