How to solve Lambert W function?

Specific Domains Numerics
18

I ran the following:

function ricky(x, k, r, I)
  for i in 1:I
    q = 1-x/k
    y = x * exp(r*q)
    x = y
  end
  return y
end
y = ricky(50000, 2.2*10^7, 0.47, 2)
# a given population increases from 50 000 to 79 914.30 between to and t1
# now, let's invert it
using LambertW
x = -(k/r)*lambertw(-r*exp(-r)*y/k)
julia> x
49999.99999999999

which looks pretty good to me…
Thank you!

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