Posted by **Erica** on Thursday, January 6, 2011 at 11:55pm.

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!!

- Calc -
**Damon**, Friday, January 7, 2011 at 2:09am
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

- Calc -
**alv**, Monday, August 27, 2012 at 6:03am
the 8th line is the simplification of the sixth line,,, im wandering why it is 45? is the algebraic solution wrong?

## Answer this Question

## Related Questions

- algebra - A cup of coffee is heated to 180°F and placed in a room that maintains...
- math calculus - In an experiment a persons body temperature is given by T=310-(7...
- Math - A group of scientists found a new species of spider in the desert. The ...
- physics - the temperature of a body falls from 30C to 20C in 5 minutes. The air...
- Algebra - A can of soda is placed inside a cooler. As the soda cools, its ...
- math - Suppose that you are a CSI and you are called to a crime scene at 12:00 ...
- algebra - A can of soda at 79°F is placed in a refrigerator that maintains a ...
- Calculus - A can of soda at 80° F. is placed in a refrigerator that maintains a ...
- Math - Natalie performs a chemistry experiment where she records the ...
- physics - A body covers 1 complete revolution around a circular park of ...

More Related Questions