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In 1950, the per capita gross domestic product (GDP) of Australia was approximately $1800. Each year afterwards, the per capita GDP increased by approximately 6.7%. Write a function that gives the approximate per capita GDP of Australia t years after 1950.

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MrEquation
The function would be: G(t) = 1800(1.067)^t

This is an exponential equation. There are in the form: y = ab^x

The a value represents the starting amount of 1800.

The b value represents the increasing rate of 1.067 (adding on 6.7%).

A function assigns values. The function that gives the approximate per capita GDP of Australia in t years after 1950 is $1800(1.065)^t.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

It is given that the GDP of Australia in 1950 was $1800, which is increasing by 6.7%, therefore, every year after 1950, the GDP of Australia will be increased by 6.5% from the previous year. This will create a compounding effect, therefore, a function that gives the approximate per capita GDP of Australia in t years after 1950 can be written as,

[tex]\rm GDP = \$1800(1+6.5\%)^t\\\\GDP = \$1800(1.065)^t[/tex]

Hence, the function that gives the approximate per capita GDP of Australia in t years after 1950 is $1800(1.065)^t.

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