(Steps Shown) Foreign Trade The rate of change of the value of goods exported from the United States between 1990 and 2001 can be modeled as E^prime(t)=-1.665 t^2+16.475


Question: Foreign Trade The rate of change of the value of goods exported from the United States between 1990 and 2001 can be modeled as

\[E^{\prime}(t)=-1.665 t^{2}+16.475 t+7.632\]

billion dollars per year

\(t\) years after the end of 1990 . Likewise, the rate of change of the value of goods imported into the United States during those years can be modeled as

\(I^{\prime}(t)=4.912 t+40.861\) billion dollars per year

\(t\) years after 1990.

  1. Find the difference between the accumulated value of imports and the accumulated value of exports from the end of 1990 through 2001 .
  2. Is your answer from part \(a\) the same as the area of the region(s) between the graphs of \(E^{\prime}\) and \(I^{\prime} ?\) Explain.

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