anonymous 5 years ago Find the solution of a discrete dynamical system

1. anonymous

hey btm I solved your problem

2. anonymous
3. anonymous

\[a _{0}=3 \]

4. anonymous

\[a _{n}=2a_{n-1}+ 2 \]

5. anonymous

thanks for that...

6. anonymous

this is another one and I have worked it out but doesn't seem to fit

7. anonymous

8. anonymous

9. anonymous

I got it

10. anonymous

a0=3 a1= 2(a0)+2 a2= 2(a1)+2 = 2[2(a0)+2]+2=2 (3 + 2 a0) a3= 2(a2)+2=2(3+2a0)+2=2 (7 + 4a0)

11. anonymous

ok...I will be back in 10 minutes...I have more if you can help

12. anonymous

a4=2 (15 + 8 a0]) At this point you should see a pattern aN= 2(2^n\[a_n=(2^n-1)+2^{n-1}a_0\]

13. anonymous

thanks...not checking out on calculator

14. anonymous

what do you mean?

15. anonymous

there is a way on graphing cal. to enter the system to check to see if the solution works

16. anonymous

it works by hand so thanks!

17. anonymous

I have two more...can you help

18. anonymous

sure,

19. anonymous

\[b _{0}=3\]

20. anonymous

\[b _{n}=.25b _{n-1}-1-n\]

21. anonymous

b1=.25*b0 - 1 - 1=0.25 (-8. +b0) b2=.25*b1 - 1 - 2=-3 + 0.25` (-2 + 0.25` b0)=0.0625 (-56. +b0) b3=-4 + 0.25 (-3 + 0.25 (-2 + 0.25 b0))=0.015625 (-312. + b0) The pattern I could figure out was \[b_n=.25^n[-( 4/9 (3* 2^{2 n} n+2^{2 n+1}-2) + b_0)\]

22. anonymous

thanks and last one

23. anonymous

\[r _{0}=3\]

24. anonymous

did you see the solution to your credit card problem?

25. anonymous

\[r _{n}=r _{n-1}+2\]

26. anonymous

have to go back and read/study it

27. anonymous

This one is rather easy

28. anonymous

r1=2+r0 r2=4+r0 r3=6+r0 I will let you figure out the pattern yourself

29. anonymous

yes it since it is linear and of order 1

30. anonymous

what year are you?

31. anonymous

ooopss have another one

32. anonymous

actually in graduate school for Educational Psychology but taking 1 credit math module for financial aid purposes...grrhhh

33. anonymous

but I'm learning some real life applications in the process

34. anonymous

\[d _{0}=3\]

35. anonymous

I am sure of the relation between psyc and this

36. anonymous

*I am not sure of the relation between psyc and this

37. anonymous

\[r _{n}=.65a _{n-1}+1.05(.5)^{n}\]

38. anonymous

I know that is why its is frustrating to figure this stuff out on my own without a professor

39. anonymous

a lot of work for 1 credit....

40. anonymous

1 credit hour?

41. anonymous

so I truly appreciate your help!

42. anonymous

YES!

43. anonymous

I don't think my uni has any 1 credit hour class

44. anonymous

approved modules for financial aid purpose...doesn't count towards degree...go figure!

45. anonymous

I remember some grad student in my physics, never knew why

46. anonymous

so frustrating but can't afford to pay out of pocket right now

47. anonymous

this is first and last semester taking this route...actually have 3 summer courses so don't have to worry about it then

48. anonymous

you going for phd?

49. anonymous

masters then maybe doctorate...

50. anonymous

did you see last problem

51. anonymous

Yea, working on it

52. anonymous

are you doing by hand

53. anonymous

most of it