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?

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

The GDP will reach $1.6 trillion in the year 2017 if the average growth rate of 3.2% is maintained.