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 $3.4 trillion?

Answer 1

Year        GDP
  y           (billion $)

1985       577

1986       577+ 3.2% of 577 = 577 * 1.032

1987       577* 1.032 + 3.2% of 577 * 1.032 = 577 * (1.032)^2

1988       577 * (1.032)^3

1989       577 * (1.032)^4

....           .... => model GDP = 577 * (1.032)^ (y - 1985)

Then, for GDP = $3.4 trillion = $3400 billion =>

3400 = 577 (1.032)^ (y - 1985)

Divide both sides by 577:

(1.032)^ (y - 1985) = 3400 / 577 = 5.892548

Apply logarith to both sides:

(y - 1985) log (1.032) = log 5.892548

=> y - 1985 = log (5.892548) / log(1.032) = 56.3 years

=> y = 1985 + 56.3 = 2041.3

Answer: 2041