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A Veterinary doctor was examining a sick...

A Veterinary doctor was examining a sick cat brought by a pet lover. When it was brought to the hospital, it was already dead. The pet lover wanted to find its time of death. He took the temperature of the cat at 11.30 pm which was `94.6^(@)F`. He took the temperature again after one hour, the temperature was lower than the first observation. It was `93.4^(@)F`. The room in which the cat was put is always at `70^(@)F`. The normal temperature of the cat is taken as `98.6^(@)F` when it was alive. The doctor estimated the time of death using Newton law of cooling which is governed by the differential equation: `(dT)/(dt) prop (T − 70),` where `70^(@)F` is the room temperature and T is the temperature of the object at time t.
Substituting the two different observations of T and t made, in the solution of the differential equation `(dT)/(dt)`=k(T-70) where k is a constant of proportion, time of death is calculated.
If t = 0 when T is 72, then the value of c is

A

`-2`

B

0

C

2

D

Log 2

Text Solution

Verified by Experts

The correct Answer is:
D
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A Veterinary doctor was examining a sick cat brought by a pet lover. When it was brought to the hospital, it was already dead. The pet lover wanted to find its time of death. He took the temperature of the cat at 11.30 pm which was 94.6^(@)F . He took the temperature again after one hour, the temperature was lower than the first observation. It was 93.4^(@)F . The room in which the cat was put is always at 70^(@)F . The normal temperature of the cat is taken as 98.6^(@)F when it was alive. The doctor estimated the time of death using Newton law of cooling which is governed by the differential equation: (dT)/(dt) prop (T − 70), where 70^(@)F is the room temperature and T is the temperature of the object at time t. Substituting the two different observations of T and t made, in the solution of the differential equation (dT)/(dt) =k(T-70) where k is a constant of proportion, time of death is calculated. If the temperature was measured 2 hours after 11.30pm, will the time of death change? (Yes/No)

A Veterinary doctor was examining a sick cat brought by a pet lover. When it was brought to the hospital, it was already dead. The pet lover wanted to find its time of death. He took the temperature of the cat at 11.30 pm which was 94.6^(@)F . He took the temperature again after one hour, the temperature was lower than the first observation. It was 93.4^(@)F . The room in which the cat was put is always at 70^(@)F . The normal temperature of the cat is taken as 98.6^(@)F when it was alive. The doctor estimated the time of death using Newton law of cooling which is governed by the differential equation: (dT)/(dt) prop (T − 70), where 70^(@)F is the room temperature and T is the temperature of the object at time t. Substituting the two different observations of T and t made, in the solution of the differential equation (dT)/(dt) =k(T-70) where k is a constant of proportion, time of death is calculated. Which method of solving a differential equation helped in calculation of the time of death?

A Veterinary doctor was examining a sick cat brought by a pet lover. When it was brought to the hospital, it was already dead. The pet lover wanted to find its time of death. He took the temperature of the cat at 11.30 pm which was 94.6^(@)F . He took the temperature again after one hour, the temperature was lower than the first observation. It was 93.4^(@)F . The room in which the cat was put is always at 70^(@)F . The normal temperature of the cat is taken as 98.6^(@)F when it was alive. The doctor estimated the time of death using Newton law of cooling which is governed by the differential equation: (dT)/(dt) prop (T − 70), where 70^(@)F is the room temperature and T is the temperature of the object at time t. Substituting the two different observations of T and t made, in the solution of the differential equation (dT)/(dt) =k(T-70) where k is a constant of proportion, time of death is calculated. State the degree of the above given differential equation.

A Veterinary doctor was examining a sick cat brought by a pet lover. When it was brought to the hospital, it was already dead. The pet lover wanted to find its time of death. He took the temperature of the cat at 11.30 pm which was 94.6^(@)F . He took the temperature again after one hour, the temperature was lower than the first observation. It was 93.4^(@)F . The room in which the cat was put is always at 70^(@)F . The normal temperature of the cat is taken as 98.6^(@)F when it was alive. The doctor estimated the time of death using Newton law of cooling which is governed by the differential equation: (dT)/(dt) prop (T − 70), where 70^(@)F is the room temperature and T is the temperature of the object at time t. Substituting the two different observations of T and t made, in the solution of the differential equation (dT)/(dt) =k(T-70) where k is a constant of proportion, time of death is calculated. The solution of the differential equation (dT)/(dt)=k(T-70) is given by,

Which is solid at room temperature