Find the solution of a discrete dynamical system

- anonymous

Find the solution of a discrete dynamical system

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- anonymous

hey btm I solved your problem

- anonymous

\[a _{0}=3 \]

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## More answers

- anonymous

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

- anonymous

thanks for that...

- anonymous

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

- anonymous

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- anonymous

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- anonymous

I got it

- 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)

- anonymous

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

- anonymous

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

- anonymous

thanks...not checking out on calculator

- anonymous

what do you mean?

- anonymous

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

- anonymous

it works by hand so thanks!

- anonymous

I have two more...can you help

- anonymous

sure,

- anonymous

\[b _{0}=3\]

- anonymous

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

- 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
\[b_n=.25^n[-( 4/9 (3* 2^{2 n} n+2^{2 n+1}-2) + b_0)\]

- anonymous

thanks and last one

- anonymous

\[r _{0}=3\]

- anonymous

did you see the solution to your credit card problem?

- anonymous

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

- anonymous

have to go back and read/study it

- anonymous

This one is rather easy

- anonymous

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

- anonymous

yes it since it is linear and of order 1

- anonymous

what year are you?

- anonymous

ooopss have another one

- anonymous

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

- anonymous

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

- anonymous

\[d _{0}=3\]

- anonymous

I am sure of the relation between psyc and this

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

a lot of work for 1 credit....

- anonymous

1 credit hour?

- anonymous

so I truly appreciate your help!

- anonymous

YES!

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

you going for phd?

- anonymous

masters then maybe doctorate...

- anonymous

did you see last problem

- anonymous

Yea, working on it

- anonymous

are you doing by hand

- anonymous

most of it

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