Using Exponential and Logarithmic Functions

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 $2.9 trillion?

Answer 1

G = G₀(1+r)^t where G represents future GDP, G₀ represents original GDP, r represents rate, and t represents time.

 

2900 = 577(1+.032)^t 

 

2900 = 577(1.032)^t

 

2900/577 = 1.032^t 

 

log (2900/577) = t*log 1.032

 

log 2900 - log 577 = t*log 1.032

 

t = (log 2900 - log 577)/(log 1.032) = (0.7012)/(0.0137) = 51.26 years

 

This means that approximately 51 years after 1985, the GDP will be 2.9 trillion dollars. That would be the year 2036