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 $1.8 trillion?

Construction of the model:

GDP = 577 * (1.032) ^ t, where GDP is in billion dollars and t is the time in years since 1985.

year     t (in years)   GDP (in billion dollars)

1985    0                   577

1986    1                   577* 1.032 = 595.46

1987    2                   577 * (1.032)^2 = 614.52

1988    3                   577 * (1.032)^3 = 634.18

?           t                   577 * (1.032)^t

Then, GDP = 1.8 trillion = 1800 billion = 577 * (1.032)^ t

=> (1.032)^t = 1800 / 577

=> t log (1.032) = log (1800 / 577)

=> t = log (1800 / 577) / log (1.032) = 36.12

Therefore, if the growth rate keeps in 3.2% per year, the GDP will equal 1.80 trillion 36 years after 1985 => 1985 + 36 = 2021.

2021