In 195019501950, the per capita gross domestic product (GDP) of Australia was approximately \$1800$1800dollar sign, 1800. Each year afterwards, the per capita GDP increased by approximately 6.7\%6.7%6, point, 7, percent.
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Complete question:
In 1950, the per capita gross domestic product (GDP) of Australia was approximately \$1800$1800dollar sign, 1800. Each year afterwards, the per capita GDP increased by approximately 6.7\%6.7%6, point, 7, percent.
Write a function that gives the approximate per capita GDP G(t) of Australia t years after 1950.
Given:
The GDP of Australia for the year 1950 was approximately $ 1800
The per capita GDP increases by approximately 6.7% each year
To find:
A function that gives the approximate per capita GDP of Australia t years after 1950
Solution:
It is given that the GDP of $ 1800 of Australia is increasing approximately by 6.7% each year
So, let's form a function to find the per capita GDP of Australia at the end of each year
t = 1 ⇒ 1800 + (6.7% of 1800) ⇒ 1800(1 + ) ⇒ 1800(1 + 0.067) ⇒ 1800(1.067)
t = 2 ⇒ [1800(1.067)] [1 + 0.067] ⇒ 1800(1.067)²
t = 3 ⇒ [1800(1.067)] [1 + 0.067] [1 + 0.067] ⇒ 1800(1.067)³
t = 4 ⇒ [1800(1.067)] [1 + 0.067] [1 + 0.067] [1 + 0.067] ⇒ 1800(1.067)⁴
......
Since we have to find the approximate per capita GDP "G(t)" of Australia after "t" years of 1950.
Therefore, by observing the above pattern, we can form the final function as follows:
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