3. The gross domestic product of a country is a measure of the total value of al

Question

3. The gross domestic product of a country is a measure of the total value of all goods and services produces in that country over a period of time. The GDP of the United States for the year 2016 was 18.57 trillion dollars. Assume that the GDP of the United States grows at a rate of 2% each year (in other words, car (a) Assuming 2% growth, what will be the GDP of the United States in the year 2017? what about in the year 2018? 2019? (b) According to this model, what will be the GDP of the United States in the year 2046 (c) Write a formula for g(t), the GDP of the United States t years after 2016.

Explanation / Answer

a) GDP in year 2016 = 18.57 trillion dollar

Annual growth = 2%

GDP = 18.57(1+ 0.02)^t

where t is no. of years

GDP = 18.57(1.02)^t

In yr 2017 ; t = 1 ; GDP = 18.94 trill $

In yr t = 2018 ; t = 2; GDP = 21.26 trill dollar

In yr t = 2019 ; t = 3 ; GDP = 19.707 trill dollar

b) In 2046 ; t= 29

GDP = 18.57(1.02)^29 = 32.977 trillion dollar

c)

GDP = 18.57(1+ 0.02)^t

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