Question

1950, 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 G(t) of Australia t years after 1950.

Answer 1

Given :

The per capita GDP in 1950 = P = $ 1800

The percentage increase in per capita each year = r = 6.7 %

The time period for increase = t years

To Find :

A function that gives the approximate per capita GDP  of Australia t years after 1950

Solution :

Let The per capita after t years = G ( t )

The per capita GDP after t years = initial amount of GDP × $(1+\dfrac{rate}{100})^{time}$

Or, G ( t ) = P  × $(1+\dfrac{r}{100})^{t}$

Or, G ( t ) = $ 1800  × $(1+\dfrac{6.7}{100})^{t}$

Or, G ( t ) = $ 1800  × $(1.067)^{t}$

∴  per capita GDP after t years = $ 1800  × $(1.067)^{t}$

Hence, The function that gives the approximate per capita GDP  of Australia t years after 1950 is  $ 1800  × $(1.067)^{t}$ Answer