Exponentials, SMB-001

In 2004 there were 13.5 million registered motor vehicles in Australia. The number of registered motor vehicles is increasing at a rate of 2.3% per year.

Find an expression that represents the number (in millions) of registered motor vehicles `(V)`, if `y` represents the number of years after 2004? (2 marks)

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`V = 13.5 xx (1.023)^y`

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`text(In 2004, 13.5 million)`

`Vtext{(1 year later)} = 13.5 xx (1.023)`

`Vtext{(2 years later)}= 13.5 xx (1.023) xx (1.023)= 13.5 xx (1.023)^2`

`:. V(y\ text{years later}) = 13.5 xx (1.023)^y`