Newton Nether Warts Hoe

'''The Newton Nether Warts Hoe is a Hoe. It can be crafted from the Mathematical Hoe Blueprint. This hoe can be upgraded to T3 by using Jacob's Tickets and can get higher tiers by harvesting Nether Wart.'''

Upgrades
Harvest +10% nether warts Gain +1% Alchemy Exp Harvest +25% nether warts Gain +2% Alchemy Exp Logarithmic Counter = Harvest +16% nether wart per digits on the Counter, minus 4! Bonus nether wart percent increases your Farmhand perk's chances
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Harvest +50% nether warts Gain +3% Alchemy Exp Logarithmic Counter = Harvest +16% nether wart per digits on the Counter, minus 4! Collection Analysis = Harvest +8% nether wart per digits of your collection, minus 4! Bonus nether wart percent increases your Farmhand perk's chances
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Tiers
Harvest +10% Nether Wart Gain +1% Alchemy Exp Reach 100k Counter for +1 Rarity! Harvest +10% Nether Wart Gain +2% Alchemy Exp Reach 10M Counter for +1 Rarity! Harvest +50% Nether Wart Gain +12% Alchemy Exp Mutated Bonus: Right Click For 10 seconds, Harvest +100% Nether Wart Mana Cost: 300 Cooldown: 180s
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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 \times 16% & otherwise \end{cases}$$
 * $$\text{Collection Analysis Bonus} =

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

Trivia

 * Since the introduction of Farming Fortune, all bonuses are applied as Farming Fortune as well, converting its previously multiplicative bonuses into additive bonuses.
 * The Rarity will increase by 1, whether you are upgrading it through crafting, or by counter(collecting nether warts). All 3 upgrades, and all 3 counter tiers are obtainable for the hoe, no matter the order you do them in. For example, if you have a Newton Nether Warts Hoe with 100k counter, it will increase to, and then you can increase it to by using the crafting recipe for , listed above, under "Upgradeable." The order you do them in does not matter, the Rarity will always increase by 1.