Police arrive at the scene of a murder at 12 am. They immediately take and record the body's temperature, which is 90o, and thoroughly inspect the area. By the time they finish the inspection, it is 1:30 am. They again take the temperature of the body, which has dropped to 87o, and have it sent to the morgue. The temperature at the crime scene has remained steady at 82o. When was the person murdered?
Let T(t) be the temperature of the body at time t; take t=0 to be 12 midnight. We have this information.
Time Body Temp. Ambient Temp. 0 hr 90 82 1.5 hr 87 82
t=-3:0.01:3; T=82+8*exp(-0.3133*t); plot(t,T) [t_D,T_D]=ginput(1) %Graphically locate the time t_D at which T=98.6 %MATLAB output from the previous command. t_D = -2.3364 T_D = 98.5614 hold on; plot(t_D,T_D,'or') %Plot the point (t_D,T_D) title('Determination of Time of Death') xlabel('Time t in hours'); ylabel('Temperature in degrees') gtext('\leftarrow T=82+e^{-0.3133*t}') %Put text on graph. gtext('(-2.3364, 98.5614)') %Put text on graph. hold offThis results in the plot below.