Question

A body of an unknown temperature was placed in a room that was held at 30°F. After 10 minutes, the body's temperature was 0°F, and 20 minutes after the body was placed in the room the body's temperature was 15°F. Estimate the body's initial temperature.


Thank you!!

Answer 1

I am going to assume that the heat flow into the body is proportional to the difference between body temp T and 30 and rate of change of T is proportional to heat flow .

dT/dt = k (30-T)

try T = -ae^-kt + 30
that is 30 at t-->oo and 30-a at t = 0
so
0 = -a e^-10k + 30
15= -a e^-20k + 30

30 = a e^-10k
45 = a e^-20 k

a = 30/e^-10k

45 = 30 (e^-20k/e^-10k)

45/30 = e^-10k

I think you can take it from there, check arithmetic

Answer 2

the 8th line is the simplification of the sixth line,,, im wandering why it is 45? is the algebraic solution wrong?