Problem forming recurrence relation

[SigmaLP]

I have the following equations:
y(t) = c(t) + i(t)
k(t+1) = i(t) + (1 − δ)*k(t)
y(t) = f(k(t)) = A*k(t) ; where A is constant
ct = c0*(0.5(1 + γ)^t + 0.5(1 + η)^t ; where γ is constant.


(a) What reccurence relation represents the evolution of capital k(t)?
(b) Determine the expression of k(t) from the recurrence found in a). You must express k(t) as a function of δ, γ, η, A, c(0) and k(0) at t=0.

How would I go about doing this?
Is a) self-explanatory and would the answer simply be k(t+1) = i(t) + (1 − δ)*k(t)?

Thanks for the help.

 

[stapel]

I have the following equations:
y(t) = c(t) + i(t)
k(t+1) = i(t) + (1 − δ)*k(t)
y(t) = f(k(t)) = A*k(t) ; where A is constant
ct = c0*(0.5(1 + γ)^t + 0.5(1 + η)^t ; where γ is constant.

(a) What reccurence relation represents the evolution of capital k(t)?

What is meant by "the evolution of capital"? Thank you!

 

[SigmaLP]

[/COLOR][/FONT]What is meant by "the evolution of capital"? Thank you!

It's in the context of my economy class, so k(t) is "the evolution of capital". Basically it's asking me to create a recurrence relation out of those 3 equations so as to have k(t) = ?. At least that's what I think it is!