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.

Answer 1

dT/dt = -0.3(T - 70)

Answer 2

\[t_{0} = 104\]

Answer 3

I had T(n) = -.03(104 - 70)

Answer 4

so same thing

Answer 5

u know differential eqns?

Answer 6

oooo...somewhat...has been a while

Answer 7

dT/(T-70) = -0.3dt

Answer 8

\[\int\limits_{104}^{T}dT/(T-70) = -0.3\int\limits_{0}^{t}dt\]

Answer 9

need to keep it basice with recurrence relations

Answer 10

ln (t-70) = -0.3ln(34)t

Answer 11

thanks though!

Answer 12

so initial t{0} = 140 right?

Answer 13

yes

Answer 14

t{n} = -0.3*[ t{n-1} - 70]

Answer 15

I havee that but can't get to work on calc

Answer 16

i havent used the calulator :) plug it in google to create a table if need be

Answer 17

gues i 'll do it by hand

Answer 18

how on google...tried wolfram once...pretty cool

Answer 19

Find a general and particular solution for the system and give the value of t(12), the temperature of the body after 24 hours.

Answer 20

i just reiterete it over and over in the right place on google

Answer 21

-.3*( 104 - 70)

-.3(-.3*( 104 - 70)-70)

-.3(-.3(-.3*( 104 - 70)-70)-70) like that