Question

The gross domestic product (GDP) of a certain country, which measures the overall size of the economy in billions of dollars, can be approximated by the function g(y) = 557y +8883, where y = 10 corresponds to the year 2010. Estimate the GDP (to the nearest billion dollars) in the given years. (a) 2007 (b) 2011 (c) 2012 (a) What value of y corresponds to the year 2007? y=O (Type a whole number.)

Answer 1

The estimated GDP in 2007 is 12782 billion dollars.

The estimated GDP in 2011 is 15010 billion dollars.

The estimated GDP in 2012 is 15567 billion dollars.

Explanation:

Consider the provided function.

`g(y) = 557y +8883`

Where y = 10 corresponds to the year 2010.

Part (b) Estimate the GDP (to the nearest billion dollars) in 2007.

If y = 10 corresponds to the year 2010 then y = 7 corresponds to the year 2007.

Substitute the value of y = 7 in the provided function.

`g(y) = 557(7) +8883`

`g(y) = 3899+8883`

`g(y) = 12782`

Hence, the estimated GDP in 2007 is 12782 billion dollars.

Part (b) Estimate the GDP (to the nearest billion dollars) in 2011.

If y = 10 corresponds to the year 2010 then y = 11 corresponds to the year 2011.

Substitute the value of y = 11 in the provided function.

`g(y) = 557(11) +8883`

`g(y) = 6127+8883`

`g(y) = 15010`

Hence, the estimated GDP in 2011 is 15010 billion dollars.

Part (C) Estimate the GDP (to the nearest billion dollars) in 2012.

If y = 10 corresponds to the year 2010 then y = 12 corresponds to the year 2012.

Substitute the value of y = 12 in the provided function.

`g(y) = 557(12) +8883`

`g(y) = 6684+8883`

`g(y) = 15567`

Hence, the estimated GDP in 2012 is 15567 billion dollars.