Veins Utilization (Upgrade)

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==Summary==
Veins Utilization is an repeatable upgrade that applies a -6% ore consumption / miner product (power of 0.94 per level) and +10% mining speed (multiple of +10% per level).  The ore consumption decreases exponentially, while the mining speed and cost in universe matrix and hashes increases linearly. The speed increasement also affects on [[Oil Extractor]] and [[Orbital Collector]]. 

==Levels==
{| class="wikitable sortable"
|-
|1||[[File:Tech_Veins_Utilization_1.png|link=https://dsp-wiki.com/File:Tech_Veins_Utilization_1.png]]||[[Veins Utilization_(Upgrade)|Veins Utilization 1]]||3601||{{RecipeItem|ItemName=Electromagnetic Matrix|ItemCount=400}}||{{RecipeItem|ItemName=Energy Matrix|ItemCount=400}}|| || || ||-6% ore consume / miner product. 
+10% mining speed.
|<nowiki>-6% ore consume / miner product (94%). </nowiki>
+10% mining speed (110%).
|
|-
|2||[[File:Tech_Veins_Utilization_2.png|link=https://dsp-wiki.com/File:Tech_Veins_Utilization_2.png]]||[[Veins Utilization_(Upgrade)|Veins Utilization 2]]||3602||{{RecipeItem|ItemName=Electromagnetic Matrix|ItemCount=1000}}||{{RecipeItem|ItemName=Energy Matrix|ItemCount=1000}}||{{RecipeItem|ItemName=Structure Matrix|ItemCount=1000}}|| || ||-6% ore consume / miner product. 
+10% mining speed.
|<nowiki>-11.6% ore consume / miner product (≈88.4%). </nowiki>
+20% mining speed (120%).
|
|-
|3||[[File:Tech_Veins_Utilization_3.png|link=https://dsp-wiki.com/File:Tech_Veins_Utilization_3.png]]||[[Veins Utilization_(Upgrade)|Veins Utilization 3]]||3603||{{RecipeItem|ItemName=Electromagnetic Matrix|ItemCount=1000}}||{{RecipeItem|ItemName=Energy Matrix|ItemCount=1000}}||{{RecipeItem|ItemName=Structure Matrix|ItemCount=1000}}||{{RecipeItem|ItemName=Information Matrix|ItemCount=1000}}|| ||-6% ore consume / miner product. 
+10% mining speed.
|<nowiki>-16.9% ore consume / miner product (≈83.1%). </nowiki>
+30% mining speed (130%).
|
|-
|4||[[File:Tech_Veins_Utilization_4.png|link=https://dsp-wiki.com/File:Tech_Veins_Utilization_4.png]]||[[Veins Utilization_(Upgrade)|Veins Utilization 4]]||3604||{{RecipeItem|ItemName=Electromagnetic Matrix|ItemCount=1600}}||{{RecipeItem|ItemName=Energy Matrix|ItemCount=1600}}||{{RecipeItem|ItemName=Structure Matrix|ItemCount=1600}}||{{RecipeItem|ItemName=Information Matrix|ItemCount=1600}}|| ||-6% ore consume / miner product. 
+10% mining speed.
|<nowiki>-21.9% ore consume / miner product (≈78.1%). </nowiki>
+40% mining speed (140%).
|
|-
|5||[[File:Tech_Veins_Utilization_5.png|link=https://dsp-wiki.com/File:Tech_Veins_Utilization_5.png]]||[[Veins Utilization_(Upgrade)|Veins Utilization 5]]||3605||{{RecipeItem|ItemName=Electromagnetic Matrix|ItemCount=2000}}||{{RecipeItem|ItemName=Energy Matrix|ItemCount=2000}}||{{RecipeItem|ItemName=Structure Matrix|ItemCount=2000}}||{{RecipeItem|ItemName=Information Matrix|ItemCount=2000}}||{{RecipeItem|ItemName=Gravity Matrix|ItemCount=2000}}||-6% ore consume / miner product. 
+10% mining speed.
|<nowiki>-26.6% ore consume / miner product (≈73.4%). </nowiki>
+50% mining speed (150%).
||
|-
|6||[[File:Tech_Veins_Utilization_6.png|link=https://dsp-wiki.com/File:Tech_Veins_Utilization_6.png]]||[[Veins Utilization_(Upgrade)|Veins Utilization ∞]]||3606||{{RecipeItem|ItemName=Universe Matrix|ItemCount=4000}}|| || || || ||-6% ore consume / miner product. 
+10% mining speed.
|Total consumption ≈<code>(73.4*0.94^(LVL-5))</code>%: 
Total speed: <code>150+10*(LVL-5)</code>%
|Can be researched infinitely*.
|}
Technically, the maximum level is 10,000.  But you'll run out of time in your life before you get anywhere close to that level, since the cost for each subsequent level increases linearly by +4,000 universe matrix and +3,600,000 hashes.  In practice, most players will never research above level 20-30.

== Research consumption ==

* Hashes cost formula for Level >= 6
** 3,600,000 * (Level - 5) Hashes

* Cost formula for Level >= 6
** 4,000 * (Level - 5) Universe Matrix
{| class="wikitable mw-collapsible"
|+Table of Research Consumption
|Level
|Blue
|Red
|Yellow
|Purple
|Green
|White
|Hashes
|1 vein mining speed (x / min)
|Vein reserves used in 1 min
|-
|0
|
|
|
|
|
|
|
|30.0
|30.0
|-
|1
|           400
|           400
|
|
|
|
|                      36,000
|33.0
|31.0
|-
|2
|        1,000
|        1,000
|        1,000
|
|
|
|                   180,000
|36.0
|31.8
|-
|3
|        1,000
|        1,000
|        1,000
|        1,000
|
|
|                   180,000
|39.0
|32.4
|-
|4
|        1,600
|        1,600
|        1,600
|        1,600
|
|
|                   480,000
|42.0
|32.8
|-
|5
|        2,000
|        2,000
|        2,000
|        2,000
|        2,000
|
|                1,800,000
|45.0
|33.0
|-
|6
|
|
|
|
|
|                        4,000
|                3,600,000
|48.0
|33.1
|-
|n
|
|
|
|
|
|4000*(n-5) 
|3,600,000*(n-5) 
|30*(1+(0.1*n))
|(Mining speed)*(0.94^(n))
|-
|7
|
|
|
|
|
|                        8,000
|                7,200,000
|51.0
|33.1
|-
|8
|
|
|
|
|
|                      12,000
|            10,800,000
|54.0
|32.9
|-
|9
|
|
|
|
|
|                      16,000
|            14,400,000
|57.0
|32.7
|-
|10
|
|
|
|
|
|                      20,000
|            18,000,000
|60.0
|32.3
|-
|20
|
|
|
|
|
|                      60,000
|            54,000,000
|90.0
|26.1
|-
|100
|
|
|
|
|
|                   380,000
|          342,000,000
|330.0
|0.7
|-
|200
|
|
|
|
|
|                   780,000
|          702,000,000
|630.0
|0.003
|-
|500
|
|
|
|
|
|                1,980,000
|      1,782,000,000
|1530.0
|0.0000000001
|-
|590
|
|
|
|
|
|                2,340,000
|      2,106,000,000
|1800.0
|2.52E-13
|-
|1000
|
|
|
|
|
|                3,980,000
|      3,582,000,000
|1800.0
|2.42E-24
|-
|10000
|
|
|
|
|
|            39,980,000
|    35,982,000,000
|1800.0
|3.42E-266
|}

==Prerequisite Technologies==

[[Category:Upgrade]]
Level	Icon	ID	Resource Consumption					Hashes	Unlocks	Net Gain (Total)
1	Insert paragraph Insert paragraph	3601	Insert paragraph 400 Insert paragraph	Insert paragraph 400 Insert paragraph				36.0k	-6% ore consume / miner product. +10% mining speed.	-6% ore consume / miner product (94%). +10% mining speed (110%).
2	Insert paragraph Insert paragraph	3602	Insert paragraph 1000 Insert paragraph	Insert paragraph 1000 Insert paragraph	Insert paragraph 1000 Insert paragraph			180k	-6% ore consume / miner product. +10% mining speed.	-11.6% ore consume / miner product (≈88.4%). +20% mining speed (120%).
3	Insert paragraph Insert paragraph	3603	Insert paragraph 1000 Insert paragraph	Insert paragraph 1000 Insert paragraph	Insert paragraph 1000 Insert paragraph	Insert paragraph 1000 Insert paragraph		180k	-6% ore consume / miner product. +10% mining speed.	-16.9% ore consume / miner product (≈83.1%). +30% mining speed (130%).
4	Insert paragraph Insert paragraph	3604	Insert paragraph 1600 Insert paragraph	Insert paragraph 1600 Insert paragraph	Insert paragraph 1600 Insert paragraph	Insert paragraph 1600 Insert paragraph		480k	-6% ore consume / miner product. +10% mining speed.	-21.9% ore consume / miner product (≈78.1%). +40% mining speed (140%).
5	Insert paragraph Insert paragraph	3605	Insert paragraph 2000 Insert paragraph	Insert paragraph 2000 Insert paragraph	Insert paragraph 2000 Insert paragraph	Insert paragraph 2000 Insert paragraph	Insert paragraph 2000 Insert paragraph	1.80M	-6% ore consume / miner product. +10% mining speed.	-26.6% ore consume / miner product (≈73.4%). +50% mining speed (150%).
6→∞	Insert paragraph Insert paragraph	3606	Insert paragraph 4000 × `(LVL-5)`					900 / 1 Insert paragraph	-6% ore consume / miner product. +10% mining speed.	Total ore consumption: =`0.94^LVL` Total mining speed: `100+10*LVL`%
Level	Insert paragraph Insert paragraph	Hashes	1 vein mining speed (x / min)	Vein reserves used in 1 min	Product per reserve	Crude Oil Seep half-life (hours)
Base			30.0	30.0	1	12.0
1		36,000	33.0	31.0	1.06	11.61
2		180,000	36.0	31.8	1.13	11.32
3		180,000	39.0	32.4	1.20	11.11
4		480,000	42.0	32.8	1.28	10.98
5		1,800,000	45.0	33.0	1.36	10.90
n	4000 * ( n - 5 )	3,600,000 * ( n - 5 )	30 * ( 1 + 0.1 * n )	30 * ( ( 1 + 0.1 * n ) * 0.94 ^ n )	1 / (0.94 ^ n )	12 / ( ( 1 + 0.1 * n ) * 0.94 ^ n )
6	4,000	3,600,000	48.0	33.1	1.45	10.87
7	8,000	7,200,000	51.0	33.1	1.54	10.89
8	12,000	10,800,000	54.0	32.9	1.64	10.94
9	16,000	14,400,000	57.0	32.7	1.75	11.02
10	20,000	18,000,000	60.0	32.3	1.86	11.14

17	48,000	43,200,000	81.0	29.6	2.86	12.72
20	60,000	54,000,000	90.0	26.1	3.45	13.79
100	380,000	342,000,000	330.0	0.7	487	530.89 (~7 months)
200	780,000	702,000,000	630.0	0.003	236826	135329 (~15.4 yrs)
500	1,980,000	1,782,000,000	1530.0	0.0000000001	2.7E13	6.42E+12 (~733 mln yrs)
590	2,340,000	2,106,000,000	1800.0	2.52E-13	7E+15	1.43E+015 (~163 bln yrs)
1000	3,980,000	3,582,000,000	1800.0	2.42E-24	7E+26	8.85E+025 (~10 sextillion yrs)
10000	39,980,000	35,982,000,000	1800.0	3.42E-266	5E+268	6.31E+266 (~7.21E+262 yrs)