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.
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
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
More Related Questions
- Maths - The body of a murder victim was discovered at 11:00 A.M. and found the ...
- Math - A group of scientists found a new species of spider in the desert. The ...
- 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...
- Trigonometry URGENT! - A group of scientists found a new species of spider in ...
- math - Suppose that you are a CSI and you are called to a crime scene at 12:00 ...
- physics - the temperature of a body falls from 30C to 20C in 5 minutes. The air ...
- math-urgent - Newton’s Law of Cooling states that the temperature of a heated ...
- Newtons Law of Cooling - using Newton's Law of Cooling: At 10:30 am the medical ...
- calculus - Newton’s law of cooling states that the rate of cooling of an object ...