In what year will humans be eating at the Earth’s current rate of npp given the following?
The net primary productivity (npp) is the total amount of energy produced in
a year as a result of photosynthesis in the entire world. It has been estimated that the npp is about 3.0*10^21 joules/year (a joule is a unit of energy equivalent to 2.39*10^-4 Calories). Given that the average person consumes about 2500 Calories per day and assuming that the human population was 5996.17 million in 1999 and continues to grow at the 1999 rate of 84 million people per year, in what year will humans be eating at the Earth’s current rate of npp?
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The net primary productivity (npp) is the amount of energy stored in the form of biomass due to photosynthesis. It is estimated to be 3.0*10^21 J. The human population in 1999 was 5996.17 million and growing at 84 million people per year. An average human consumes 2500 calories per day or 4184 J. The consumption in a year of 365 days is 1527196 J.
Starting with 5996.17*10^6 in 1999 and growing at 84*10^6 per year, the population of the Earth after n years is 5996.17*10^6 + n*84*10^6. The consumption of energy by them in a year would be `(5996.17*10^6 + n*84*10^6)*1527196` J
If this is equal to 3.0*10^21, the value of n can be determined by solving
`(5996.17*10^6 + n*84*10^6)*1527196 = 3.0*10^21`
=> n = `(((3.0*10^21)/1527196) - 5996.17*10^6)/(84*10^6)`
=> `n ~~ 23385457`
(The Earth can feed humans for over 23 million years)
The rate of energy consumed by humans would equal the npp after approximately 23385457 years
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