Question Below. Please solve with steps.

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 $2.8 trillion?

Answer 1

This problem exhibits exponential growth since the GDP grows at the same rate every year. The equation would follow this format:

 

G = G₀(1+r)^t 

 

G represents present GDP, G₀ represents initial GDP, r represents the rate of increase in decimal form, and t represents time. In this case the equation would be:

 

2800 = 577(1+.032)^t or

 

2800 = 577(1.032)^t

 

Solve for t

 

2800/577 = 1.032^t

 

4.853 = 1.032^t

 

log 4.853 = t*log 1.032

 

t = (log 4.853)/(log 1.032) = 50.15 years

 

This means that approximately 50 years after 1985, the GDP will be $2.8 trillion. That year would be 2035.