Question

From data gathered in the period 2008−2012, the yearly value of U.S. exports can be modeled by the function E(x) = −228x3 + 2,252.8x2 − 6,098.5x + 11,425.8 where x is the number of years after 2008 and E(x) is the value of exports in billions of dollars. The yearly value of U.S. imports can be modeled by the function I(x) = −400.4x3 + 3,954.4x2 − 11,128.8x + 17,749.6 where x is the number of years after 2008 and I(x) is the value of imports in billions of dollars. Estimate the total value the U.S. imported and exported in 2012. Round to the nearest whole number. About billion dollars were imported and exported by the U.S. in 2012.

Answer 1

The total value the U.S. imported and exported is 19364 billion dollars

Explanation:

* Lets explain how to solve the problem

- The yearly value of U.S. exports can be modeled by the function

E(x) = −228 x³ + 2,252.8 x² − 6,098.5 x + 11,425.8

# x is the number of years after 2008

# E(x) is the value of exports in billions of dollars

- The yearly value of U.S. imports can be modeled by the function

I(x) = −400.4 x³ + 3,954.4 x² − 11,128.8 x + 17,749.6

# x is the number of years after 2008

# I(x) is the value of imports in billions of dollars

* We need to calculate the total value the U.S. imported and

exported in 2012

∵ x is the number of years after 2008

∴ At 2012 x = 4 years

- Lets calculate the value of the exports in 2012

∴ E(x) = -228(4)³ + 2,252.8(4)² - 6,098.5(4) + 11,425.8

∴ E(x) = 8484.6 billion dollars

- Lets calculate the value of the imports in 2012

∴ I(x) = -400.4(4)³ + 3,954.4(4)² - 11,128.8(4) + 17,749.6

∴ I(x) = 10879.2 billion dollar

∵ The total value the U.S. imported and exported = E(x) + (I(x)

∴ The total value = 8484.6 + 10879.2 = 19363.8

∴ The total value = 19364 billion dollars

* The total value the U.S. imported and exported is 19364 billion dollars