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Math 111)0 Homework 24 13 November, 2013 Key Name: 1. (12 points) Newton’s law of cooling (or warming) states that the rate of change of tein— perature u of an object is proportional to the temperature difference between the obcct and its surroundings. That is, =k(u—T) where T is the constant. temperature of the surroundings and k is sonic constant. Suppose an object at 00 C is placed in a room where the temperature is 30° C. If the temperature of the 01) ject is 12° C after 1 hour, how long will it take for the object to reach 27° C? poi4I: I kd6 O t i _____ lrIL4—TI Sc tL..C t’-t (G,.) , kG ti AO 3Oe kc y 4-fklpkfltA c t-t -(-r) k 1 (DOV’ T- 3 _ O ek i c 3O-3 1 Oe’ T - A T÷Akt 27-3P° — -3 -30e -T—Ae 1)0 used to estunate tune of death (though the 700 estimate is likely to be quite rough). Suppose a corpse is (liscovered at 110011 ill a F 10011) and at that time the body temperature is 96.10 F. If at 1:00 PM the body F, use Newton’s law of cooling to estimate time tine of (heath. (You temperature is may assume that time body temperature was 98.6° F when alive.) 2. (12 points) Newton’s law of cooling can k(-r) (ç Ak L4 Poiit: (O/1(o.i) T $‘.c S (t oL 1) &-o 1L’L’$ w111 ,. 70 A -ir-- ,Te — 96.1 -zi z4 ‘V.( e 7Oke° -1- A A 7O.I q 7OZ.I Z 14 zt ek •q2s3 ek k ((.q-zc3 —.os11’r ‘‘ w -1,5G So .5514O 50 ” t J Dccv-cc 37.7 cd- 10:27/v.,.