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Question: the normal body temperature for cats varies over a narrow...

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The normal body temperature for cats varies over a narrow range of temperatures. One cat has a history of a body temperature of 38.7^\circ{\rm C} . One night this cat is hit by a car at some time during the night. The dead cat is discovered at 7 AM, and a young scientist wants to determine the time of death of the poor cat. He measures the temperature of the cat and finds that the body temperature of the cat is 23^\circ{\rm C} (H(0) = 23). For this problem, t = 0 corresponds to 7 AM. The early morning temperature is found to be 16^\circ{\rm C} . Newton's Law of Cooling with a constant environmental temperature (T_e = 16) gives the differential equation:

\frac{dH}{dt} = -k_1(H - 16), \qquad H(0) = 23



a. where H(t) is the body temperature of the cat and k_1 is a kinetic constant of cooling. Find the solution to this differential equation with its initial condition (including the cooling constant k_1 written as 'k1').

H(t) =  .

b. If one hour later the temperature of the body is found to be 21^\circ{\rm C} (H(1) = 21), then determine the value of the constant of cooling, k_1 , in the differential equation.

k_1 =  .

c. Find the time t_d when the death occurs and give the time on the clock.

t_d =  .
Time on the clock =  :  AM,
where the minutes are a decimal value with at least 4 significant figures.

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