Answer:
a) The yearly energy consumption for a US population of 300 million is ![3\times 10^{16} J/year](https://tex.z-dn.net/?f=3%5Ctimes%2010%5E%7B16%7D%20J%2Fyear)
b) The energy that would be released if a 60 kg person were converted entirely into energy is
Joules.
c) 180 years would this amount of energy support a population of 300 million.
Explanation:
a) Average energy consumed by single person of US = 100,000,000 J/year
Then 300 million US citizen will consume:
300 million = 300 × 1,000,000 = ![3\times 10^8](https://tex.z-dn.net/?f=3%5Ctimes%2010%5E8)
The yearly energy consumption for a US population :
![100,000,000 J/year\times 3\times 10^8=3\times 10^{16} J/year](https://tex.z-dn.net/?f=100%2C000%2C000%20J%2Fyear%5Ctimes%203%5Ctimes%2010%5E8%3D3%5Ctimes%2010%5E%7B16%7D%20J%2Fyear)
The yearly energy consumption for a US population of 300 million is ![3\times 10^{16} J/year](https://tex.z-dn.net/?f=3%5Ctimes%2010%5E%7B16%7D%20J%2Fyear)
b) ![E = m\times c^2](https://tex.z-dn.net/?f=E%20%3D%20m%5Ctimes%20c%5E2)
E = Energy from converted mass of m
c = speed of light
Given mass of person = m = 60 kg
![E=60 kg\times (3\times 10^8 m/s)^2 = 5.4\times 10^{18} J](https://tex.z-dn.net/?f=E%3D60%20kg%5Ctimes%20%283%5Ctimes%2010%5E8%20m%2Fs%29%5E2%20%3D%205.4%5Ctimes%2010%5E%7B18%7D%20J)
c) Energy calculated in part (b) = ![E=5.4\times 10^{18} J](https://tex.z-dn.net/?f=E%3D5.4%5Ctimes%2010%5E%7B18%7D%20J)
The yearly energy consumption for a US population of 300 million in an year = ![3\times 10^{16} J/year](https://tex.z-dn.net/?f=3%5Ctimes%2010%5E%7B16%7D%20J%2Fyear)
Let the that would be supported by
Joules of energy be x.
![x\times 3\times 10^{16} J/year=5.4\times 10^{18} J](https://tex.z-dn.net/?f=x%5Ctimes%203%5Ctimes%2010%5E%7B16%7D%20J%2Fyear%3D5.4%5Ctimes%2010%5E%7B18%7D%20J)
![x=\frac{5.4\times 10^{18} J}{3\times 10^{16} J/year}=180 years](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B5.4%5Ctimes%2010%5E%7B18%7D%20J%7D%7B3%5Ctimes%2010%5E%7B16%7D%20J%2Fyear%7D%3D180%20years)
180 years would this amount of energy support a population of 300 million.