Gross Domestic Product per capita (GDP/Population or GDPpc) is widely used by economists as a measure of an economy's (society's) productivity (and therefore it's wealth). As with any socioeconomic variable, measuring the growth of GDPpc and examining the determinants of this growth are important questions, especially with regards to the role of energy consumption as a driver of the economy's productivity. GDPpc can be "decomposed" (or separated) into: GDP Energy_ GDP (1) Pop Pop Energy where Energy denotes total energy consumption. The variable (GDP/Energy) is known as "energy intensity" and measures how much energy is used in generating one unit of GDP (typically measured in inflation-adjusted dollars); the ratio (Energy/Pop) measures how much energy the population of a county/economy/society consumes as a result of its lifestyle and consumption choices. Let's relabel the variables as follows: GDP _ - = G(t), Energy = E(t), GDP = 1(t), Pop Pop Energy where we also make it explicit that the variables are time-dependent (with the unit of time being one year). Taking the natural logarithm of equation (1) we get: In [ G(t)] = In [E(t)] + In[x(1)]. (2) Taking the time derivative of equation 2 we obtain: d In [G(1) ] = d In[E(1)]+ at d In [ x(1) ] , (3) = + TL (4) Relabeling the three growth rates in equation (4) we have: (5)in which the growth rate of the productivity of an economy is the result of the growth rate in energy intensity (how efcient the economy is in turning energy into economic output) and how much energy the society (its citizens, rms and organizations) consume. Now let's get empirical! The Energy Information Administration (EIA) of the U.S. Department of Energy (DOE) provides data on total yearly energy consumption by the U.S. from 1795 to 2020; the Bureau of Economic Analysis of the U.S. Department of Commerce provides data on the GDP (measured in 2009 dollars) and population of the U.S. for the same period. The excel le \"USA GDPpc EINT Energy'p-c 1795 2020) data on Total Primary Energy Consumption per Capita, GDP per unit of energy (energy intensity) and GDP per capita (measured in 2012 dollars). 1. Using the \"log difference\" method for calculating growth rates, what was the annual growth rate of GDP/Pop, Emery/Pop and GDPEner-gy for 1805 2020, 1805 1900, 1900 1949, 1950 2000, 2000 2020 (show the percentages in a table). 2. From the perspective of someone who is concern about sustainability, what does the decomposition of the growth rate of GDP/pop in question (1) for the 1805 - 2020 period informs us about? [Write a few sentences] 3. From the perspective of someone who is concern about sustainability, what does the decomposition of the growth rate of GDP/pop in question (1) for the 2000 2020 period informs us about? [Write a few sentences]