Question

Please Help!

https://gyazo.com/48ab7c5112246a7a8a9d16ac83aa8c46
For part A I tried factoring, but I didn't get anywhere with that.

Answer 1

If your sequence attains equilibrium then that means \(P_{n}=P_{n+1}\)

Use this ^

Answer 2

I tried multiplying RP_n inside the bracket and got P_n+1 = RP_n - RP_n^2

Answer 3

Don't do that, it'll make it more complicated
Check this-
\(P_{n+1}=RP_n(1-P_n)\)
Using the equilibrium condition u can write it like this-
\(P_n=RP_n(1-P_n)\)
\(P_n -RP_n(1-P_n)=0\)
\(P_n(1-R(1-P_n))=0\)
From here you can figure out the solutions

Answer 4

Wait, but what happened to the P_n+1?

Answer 5

p_n+1 is equal to P_n is because we're considering the equilibrium condition

Answer 6

I see.
So I get this:
1-R(1-P_n)
1-R+RP_n = 0
RP_n = 1+R
P_n = 1+R/R
So, P = 1+R/R
But that doesn't equal 1-R/R

Answer 7

Check your 3rd step again

Answer 8

I still don't see what I did wrong :/

Answer 9

I just took it to the other side

Answer 10

Shouldn't it be this : \(\color{red}-1+R\)

Answer 11

Oh, my bad. Sorry about that

Answer 12

That's alright you'll get the answer now :-)

Answer 13

How do I do part b?

Answer 14

Like how would you graph it? It just gives me the values P_0 = 0.25 and R = 1.5 then it wants me to plot 20 points.