Compounding problem- express the gdp of this country as a function of the number of years t after 2000. Word problem below

The gross domestic product of a certain country was $500 billion at the beginning of the year 2000 and increases at the rate of 2.3% per year. (think of this as a compouding problem)

express the gdp of this country as a function of the number of years t after 2000.

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GDP at year 2000 = $500 Billion

The increase rate of GDP is 2.3% per year.

GDP at year 2001 `= ($500B)+($500B)xx2.3/100 = ($500B)xx1.023`

This is one year after 2000

GDP at year 2002 `= (($500B)xx1.023)xx1.023 = ($500B)xx1.023^2`

This is two years after 2000

*If the year is t years after 2000 we can say the GDP is;*

`GDP = ($500B)xx1.023^t`

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