How can I find the value of k(subscript t+1) for periods t=1...50?

[Gribouillis]

Use a "for" loop to compute the sequence

>>> delta, s, theta = 0.08, 0.3, 0.35
>>> k = 2.5
>>> for i in range(10):
...     k = (1 - delta) * k + s * k ** theta
...     print(f"{i:3d}: {k}")
... 
  0: 2.7134283534178376
  1: 2.9218081528946036
  2: 3.124679201001941
  3: 3.321700371622801
  4: 3.512629012329435
  5: 3.69730401824454
  6: 3.8756318212738003
  7: 4.04757472314622
  8: 4.2131411328686434
  9: 4.372377365759764
>>>