Question

A dead body was found within a closed room of a house where the temperature was a constant 22° C. At the time of discovery the core temperature of the body was determined to be 27° C. One hour later a second measurement showed that the core temperature of the body was 25° C. Assume that the time of death corresponds to t = 0 and that the core temperature at that time was 37° C. Determine how many hours elapsed before the body was found. [Hint: Let  t₁ > 0 denote the time that the body was discovered.] (Round your answer to one decimal place.)

____ hr

Answer 1

front of di/dt tell that flee thimper Gian thou MO con ese necoton's low of cooling to determine when the body was givern that discovered ) من -temperation of the room is 22° ce M22) the temperature of the body to is 32 Let T(0) = 37 At some time it be the body is discovered with a temperature of 22 degrees At ttl cone hour later) the temperane is 25 degrees "Mewton's law of cooling it -dł dt =le(M-T) we gian mano also negative sign in decreges with time di dr = 6 (22-1) eusing separation of wriables we ger It di a fo belt Integrating thoth sides we get

In 192-1) =-ck+tc) wring properties of logg we can write elet lette 22-T LA - -ce 2-T the reciprocal of both sides How taking we get اعا ۔ 22-T =-ce Solve forī -ke ał =-22-le dividing through by negative's T= 22 +cekt how at t=0 the temperature is 37 37 = 22.7ce solving far c we get E= 15' tina the son of the temperature at any T(+) = 22 +15 ékt To find out.k is :- the some time it the temp is 22 degrees hourlater it is 25 degrees

27 2) IS at feu fivewean "5 = 2 +15 pill(t+1) looking sobivalt 22 Korom both sides - 15 ekt okt KU log face tou natural of both side, In 17 l = lnetar H-60443 ki = lnl Chris eu3 1.0986122 how looking at the second san 25 = 22 +15.e 5.ek(+1) distobune theik'in tu exponu -kt-k 25 = 22 +15.ekt Sub tract ar from both sides 3 =15.8kt le -krok T5 -kille intis we have kta taifexqu£1:09 86122 Plug this in and save fark

-1.0986122 -k : kohted + RR 5-1.0986122 +1.60043 c=0-5108178 no tow we have 'k' our eauation for the teuperabre retary fint in T(+) = 22 +15.é 0-5108178+ Snow we know that wonten bodjeza found the temp was 27 degreen. To find much time has clapsed death has occured we says do the following 27 = 22 +15.80-51081787 s love for it +Ž 1- 8310077