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There are three ways to burn $FERT—by fertilizing FarmLand, sending a Roostr to forage, and by fertilizing Resources on FarmLand to increase the chance of being foraged.
The main burn mechanism comes from FarmLand fertilization. Fertilizing FarmLand causes its reward multiplier to increase in increments of 0.25x, up to a maximum of 16x. Note that all FarmLand have an initial reward multiplier of 4x.
The amount of $FERT required to increase the FarmLand multiplier is based on a continuous diminishing returns function, converted to a step-wise approximation.
n = 0.75 (set to some constant)
x = $FERT burned
F = 0.0002 (initial fertility increase per $FERT burned)
Base = 4 (initial multiplier value)
Putting all those values in, we get the following function for the multiplier increase based on $FERT burned:
This is then converted to a step-wise function based on every 0.25x increase in fertility multiplier. To move from a base multiplier of 4x to the next step at 4.25x, players need to burn 1,372 $FERT. The step from 15.75x to the maximum at 16x requires 1,275,000 $FERT to be burned.
$FERT burn required to achieve multiplier steps
$FERT is also burned through Foraging. Just as sending chikn to forage requires players to burn a fixed amount of $EGG, sending Roostr to forage requires players to spend a fixed amount of $FERT.
Foraging also allows players to burn $FERT to increase the chance that a Resource will be found. The chance of a successful Forage on an individual Resource can be increased by between 0.0050% and 0.0100% per $FERT burned, up to a maximum boost of 10%. This boost lasts 28 days before requiring refertilization.