Hello all, I have a question that I feel like is very simple and I am just overthinking it. First time posting here, so if my post seems off let me know!
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Coal reserves in a country in 2018 are 11,750 Quads. Coal used in this country is expected to grow at an exponential rate over the next 100 years. The present rate of coal use is 0.5 Quads per year and is expected to increase to 15 Quads per year after a hundred years. Calculate:
a) When the coal reserves in this country will be 50% depleted
b) When the coal reserves in this country will be completely depleted
c) If the rate of consumption was constant and not exponential at 15 Quads per year, in what year would the coal reserves be completely depleted?
HINT: Exponential production/consumption has the form C = C{_o}exp^{lambda T} where T is the time in years.
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This is for an energy course I am taking and we haven't really encountered any math yet, so seeing this question I can't decide if I am underthinking or overthinking things! Especially for the first part. Part a wants us to determine when coal reserves will be 50% depleted (the amount of years it would take for this to happen). It gives us the rate of consumption at T = 0 (0.5 Quads/year) and gives us the rate of consumption at T = 100 (15 Quads/year). Lambda is the rate of change, but the rate of change is itself changing with time. I'm guessing an integral is somehow needed, but my 1st year math skills are a little rusty.
Any help guys? Thanks a lot!
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Coal reserves in a country in 2018 are 11,750 Quads. Coal used in this country is expected to grow at an exponential rate over the next 100 years. The present rate of coal use is 0.5 Quads per year and is expected to increase to 15 Quads per year after a hundred years. Calculate:
a) When the coal reserves in this country will be 50% depleted
b) When the coal reserves in this country will be completely depleted
c) If the rate of consumption was constant and not exponential at 15 Quads per year, in what year would the coal reserves be completely depleted?
HINT: Exponential production/consumption has the form C = C{_o}exp^{lambda T} where T is the time in years.
--------------------------------------------
This is for an energy course I am taking and we haven't really encountered any math yet, so seeing this question I can't decide if I am underthinking or overthinking things! Especially for the first part. Part a wants us to determine when coal reserves will be 50% depleted (the amount of years it would take for this to happen). It gives us the rate of consumption at T = 0 (0.5 Quads/year) and gives us the rate of consumption at T = 100 (15 Quads/year). Lambda is the rate of change, but the rate of change is itself changing with time. I'm guessing an integral is somehow needed, but my 1st year math skills are a little rusty.
Any help guys? Thanks a lot!
