Mathematics
Eddie
36

The annual Gross Domestic Product (GDP) of a country is the value of all of the goods and services produced in the country during a year. During the period 1985-1999, the Gross Domestic Product of the United States grew about 3.2% per year, measured in 1996 dollars. In 1985, the GDP was $577 billion. I what year did/or will the GDP equal $1.6 trillion?

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(1) Answers
head1

Given: GDP = $577 billion = $0.577 trillion in 1985. Annual growth rate = 3.2% = 0.032 After 1 year, the GDP will be  $ 0.577(1.032) trillion After 2 years, the GDP will be $ 0.577(1.032)² trillion ... After n years, the GDP will be $ 0.577(1.032)ⁿ trillion. The number of years required from 1985 for the GDP to reach $ 1.6 trillion is determined by 0.577(1.032)ⁿ = 1.6 1.032ⁿ = 1.6/0.577 = 2.773 n ln(1.032) = ln(2.773) n = ln(2.773)/ln(1.032) = 32.4 years From 1985, the year is 1985 + 32.4 = 2017.4 Answer: The GDP will reach $1.6 trillion in the year 2017 if the average growth rate of 3.2% is maintained.

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