3. (l pt.) The U.S. coal industry, under increasing pressure from tougher antipo

Question

3. (l pt.) The U.S. coal industry, under increasing pressure from tougher antipollution rules, is ratcheting up its export business. The rate of change of coal exports from 2010 through 2012 is given by (-31.863- million short tons (2000 lb) per year in year t, where t is measured in years, with t-0 corresponding to 2010. U.S. coal exports in 2010 were 81.7 million short tons. Find the function f(t) that gives the US. coal exports in year t . a. b. Assuming that the trend continued through 2013, what were U.S. coal exports for that year?

Explanation / Answer

3)

a)

in 2010, f(0) =81.7

f(t)=f(0) +r(t) dt

f(t)=81.7 +(31.863t-0.61) dt , where unit of f(t) is million short tons and 0 t 2

f(t)=81.7 +(31.863/(-0.61+1))t-0.61+1

f(t)=81.7 +81.7t0.39

f(t)=81.7*(1+t0.39)

b)

t=3 corresponds to the year 2013

f(3)=81.7(1+ 30.39)

f(3)=207.1

U.S .coal exports in 2013 is 207.1 million short tons

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