1. Express the following in log-linear form: take the natural logarithm of both
ID: 2874713 • Letter: 1
Question
1. Express the following in log-linear form: take the natural logarithm of both sides and simplify. Greek letters are constants. a) Y = zKN1 b) Z = 5e XX2 2. Compute the following first derivatives:
a) Y (X) = ln X + ln (1 X)
b) u(c) = c 1 1
c) h(w) = (6w 3 + 17w 4)
3. Go to https://www3.epa.gov/climatechange/ghgemissions/inventoryexplorer/. Under “Economic Sectors” select “All Sectors.” Under gases, choose “All gases,” then break out by “Economic sector,” then select “All years.” Use the link beneath the there is a link to download the data in .csv format.
(a) Compute each sector’s percentage of total emissions of GHG equivalents for the year 1990, and for the year 2014. Which sector saw the largest growth in terms of its original share of total emissions? Which saw the lowest growth (this could be negative)?
(b) In what year since 1990 did total emissions of GHG equivalents peak?
Explanation / Answer
1. a) Y = zKN1
=> ln Y = ln (zKN1)
=> ln Y = ln {(zKN11)}
=> ln Y = ln + ln (zKN11)
b) Z = 5e XX2
=> ln Z = ln (5e XX2)
=> ln Z = ln5 + ln (e XX2)
=> ln Z = ln 5 + XX2
a) Y (X) = ln X + ln (1 X)
Derivative, Y '(X) = 1/X - 1/(1-X)
c) h(w) = (6w 3 + 17w 4)
Derivative, h '(w) = (-18w2 + 17)
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