Simulate lollipop farming

import math

def lps(planted):
    """Lollipops per second."""
    return math.ceil(100*(1-math.exp(-(planted-20)/5000)))



###########
# The question is, what is the optimal number of lollipops to plant so that we can reach 5000 lollipops on-hand?
# I think this is a Golden Mean Bisection problem.
def plantuntil(intialPlanted, untilPlanted, mult=3, pops=0):
    seconds = 0
    lollipops = pops
    planted = intialPlanted
    while planted < untilPlanted:
        seconds += 1
        lollipops += lps(planted)*mult
        nowPlant = min(lollipops, untilPlanted - planted)
        lollipops -= nowPlant
        planted += nowPlant
    while lollipops < 5000:
        seconds += 1
        lollipops += lps(planted)*mult
    return seconds

initialPlanted = 1554
initialOwned = 2673
mult = 3*3
best = 1000
besti = 0
for i in range(initialPlanted,5000):
    candidate = plantuntil(initialPlanted, i, mult=mult, pops=initialOwned)
    if candidate <= best:
        best = candidate
        besti = i
        #print(i, candidate)

print(besti) #2920