The temperature of a body is measured as 104oF. It is observed that the amount the temperature changes for each period of two hours is -0.3 time the difference between the previous period's temperature and the room temperature, which is 70oF.
a. Write a recurrence relation for tn, the temperature of the body at the end of n 2-hour time periods.
b. Find a general and particular solution for the system and give the value of t(12), the temperature of the body after 24 hours.
c. Does this system have an equilibrium value? If so, what is it?

Question

The temperature of a body is measured as 104oF. It is observed that the amount the temperature changes for each period of two hours is -0.3 time the difference between the previous period's temperature and the room temperature, which is 70oF. 
a.	Write a recurrence relation for tn, the temperature of the body at the end of n 2-hour time periods. 
b.	Find a general and particular solution for the system and give the value of t(12), the temperature of the body after 24 hours. 
c.	Does this system have an equilibrium value? If so, what is it?

dumbcow · Answer

Tn = Tn-1 - 0.3(Tn-1 - 70)
Tn = 0.7Tn-1 + 21

t(n) = 34(.7)^n + 70
t(12) = 70.47