Question

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?

Answer 1

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.

Answer: 2021