##### This exercise uses Newton's Law of Cooling.

label Algebra
account_circle Unassigned
schedule 1 Day
account_balance_wallet \$5

Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Immediately following death, the body begins to cool. It has been determined experimentally that the constant in Newton's Law of Cooling is approximately k = 0.1947, assuming time is measured in hours. Suppose that the temperature of the surroundings is 65°F.
(a) Find a function T(t) that models the temperature t hours after death.
 T(t) =

(b) If the temperature of the body is now 71°F, how long ago was the time of death? (Round your answer to the nearest whole number.)

hr

Jul 15th, 2015

T(t) = Ta + (To - Ta)e^-kt.....where Ta is the ambient temperature, To is the initial temperature and t is time.

then, T(t) = 55 + (98.6 - 55)e^-0.1947t

=> T(t) = 55 + 43.6e^-0.1947t

so, 73 = 55 + 43.6e^-0.1947t

=> e^-0.1947t = 18/43.6

=> -0.1947t = ln(18/43.6)

so, t = -[ln(18/43.6)]/0.1947 => 4.54 hours

Please let me know if you nea case for torture by michale levined any clarification. I'm always happy to answer your questions.
Jul 15th, 2015

...
Jul 15th, 2015
...
Jul 15th, 2015
Oct 23rd, 2017
check_circle