## anonymous 5 years ago 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.

1. anonymous

dT/dt = -0.3(T - 70)

2. anonymous

$t_{0} = 104$

3. anonymous

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

4. anonymous

so same thing

5. anonymous

u know differential eqns?

6. anonymous

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

7. anonymous

dT/(T-70) = -0.3dt

8. anonymous

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

9. anonymous

need to keep it basice with recurrence relations

10. anonymous

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

11. anonymous

thanks though!

12. amistre64

so initial t{0} = 140 right?

13. anonymous

yes

14. amistre64

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

15. anonymous

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

16. amistre64

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

17. anonymous

gues i 'll do it by hand

18. anonymous

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

19. anonymous

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

20. amistre64

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

21. amistre64

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