Gauss Carrot Hoe

The Gauss Carrot Hoe is a Hoe. It can be crafted from the Mathematical Hoe Blueprint. This hoe can be upgraded by Jacob's Ticket as well as by reaching certain milestones on the internal Counter, and thus it can naturally reach a maximum rarity of.

Upgradeable
Harvest +10% carrot Gain +1% Farming Exp Harvest +25% carrot Gain +2% Farming Exp Logarithmic Counter = Harvest +16% carrot per digits on the Counter, minus 4! Bonus carrot percent increases your Farmhand perk's chances
 * -|Common Stats=
 * -|Uncommon Stats=

Harvest +50% carrot Gain +3% Farming Exp Logarithmic Counter = Harvest +16% carrot per digits on the Counter, minus 4! Collection Analysis = Harvest +8% carrot per digits of your collection, minus 4! Bonus carrot percent increases your Farmhand perk's chances
 * -|Rare Stats=

Tiers
Harvest +10% carrot Gain +1% Farming Exp Reach 100k Counter for +1 Rarity! Harvest +10% carrot Gain +2% Farming Exp Reach 10M Counter for +1 Rarity! Harvest +10% carrot Gain +3% Farming Exp Reach 100M Counter for +1 Rarity!
 * -|Common Stats=
 * -|Uncommon Stats=
 * -|Rare Stats=

Formulas
The number of digits on the counter may be calculated using:
 * $$n = \left\lfloor\log_{10} counter\right\rfloor + 1$$

In order to mathematically represent the and  ability scaling, the following formula has to be used:
 * $$\text{Logarithmic Counter Bonus} =

\begin{cases} 0 & n \leq 4 \\ (n - 4) \times 16% & otherwise \end{cases}$$
 * $$\text{Collection Analysis Bonus} =

\begin{cases} 0 & n \leq 4 \\ (n - 4) \times 8% & otherwise \end{cases}$$