Question

Let yn+1 = -0.6yn. Solve the given difference equation in terms of the initial value y0. Describe the behavior of the solution as n--> positive infinity.

Answer 1

haven't learned it yet... but this is a part of mathematical biology.

Answer 2

Observe that y_{n+1}/y_n = -0.6, a constant. This tells us that the sequence {y_n} is a geometric sequence with common ratio r = -0.6, so the solution is

y_n = (y_0) (-0.6)^n, n = 0, 1, 2, ...

Answer 3

what happens when n goes to infinity ?

Answer 4

yn goes to 0?

Answer 5

yes :)

Answer 6

Alright, thanks for the help :)