I don't know if this is calculus or if it goes in another section. I don't even know if my title is correct...sorry.
I would like to know what kind of formulas would solve the following problem.
There is a resource being produced by unit A at a rate of 2 resource per 2 seconds per unit A. So if there are 5 of unit A, then there are 10 resources being created every 2 seconds.
Unit A is produced by unit B at a rate of 2 unit A per 6 seconds for every Unit B. So if there are 5 of unit B, then every 6 seconds there are 10 of unit A produced, which in turn will start creating more resources.
Unit B is produced by unit C at a rate of 2 unit B per 18 seconds for every Unit C.
Unit C is produced by unit D at a rate of 2 unit C per 54 seconds for every Unit D.
In other words, D adds to the value of C which adds to the value of B which adds to the value of A which adds to the value of resources.
Here is the question.
In scenario 1, we start with 10,200 of unit C at time = 0.
In scenario 2, we start with 1 of unit D at time = 0.
It's pretty simple to calculate that it will take 76.5 hour until scenario 2 has the same value for unit C. But here's the question that I have no idea how to tackle: How long will it take before scenario 2 has produced more total resources than scenario 1?
I would like to know what kind of formulas would solve the following problem.
There is a resource being produced by unit A at a rate of 2 resource per 2 seconds per unit A. So if there are 5 of unit A, then there are 10 resources being created every 2 seconds.
Unit A is produced by unit B at a rate of 2 unit A per 6 seconds for every Unit B. So if there are 5 of unit B, then every 6 seconds there are 10 of unit A produced, which in turn will start creating more resources.
Unit B is produced by unit C at a rate of 2 unit B per 18 seconds for every Unit C.
Unit C is produced by unit D at a rate of 2 unit C per 54 seconds for every Unit D.
In other words, D adds to the value of C which adds to the value of B which adds to the value of A which adds to the value of resources.
Here is the question.
In scenario 1, we start with 10,200 of unit C at time = 0.
In scenario 2, we start with 1 of unit D at time = 0.
It's pretty simple to calculate that it will take 76.5 hour until scenario 2 has the same value for unit C. But here's the question that I have no idea how to tackle: How long will it take before scenario 2 has produced more total resources than scenario 1?