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 $g(y)=560y+8853$, where $y=10$ corresponds to the year 2010. Estimate the GDP (to the nearest billion dollars) in the given years.
(a) 2002
(b) 2010
(c) 2015
(a) What value of $y$ corresponds to the year 2002?
$y=2$
(Type a whole number.)
The GDP in 2002 is about $\mathrm{\$}9,973$ billion.
(b) What value of $y$ corresponds to the year 2010?
$y=10$
(Type a whole number.)
The GDP in 2010 is about $\mathrm{\$}14,453$ billion.
(c) What value of $y$ corresponds to the year 2015?
$y=15$
(Type a whole number.)
The GDP in 2015 is about $\mathrm{\$}18,230$ billion.
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Step 1 ：First, we need to find the corresponding $y$ values for the years 2002, 2010, and 2015. Since $y=10$ corresponds to the year 2010, we can calculate the $y$ values for the other years as follows: $y_{2002}=2$, $y_{2010}=10$, and $y_{2015}=15$.

Step 2 ：Next, we substitute these $y$ values into the function $g(y)=560y+8853$ to calculate the GDP for each year.

Step 3 ：For the year 2002, we substitute $y=2$ into the function to get $g(2)=560\ast 2+8853=9973$. So, the GDP in 2002 is about $\mathrm{\$}9,973$ billion.

Step 4 ：For the year 2010, we substitute $y=10$ into the function to get $g(10)=560\ast 10+8853=14453$. So, the GDP in 2010 is about $\mathrm{\$}14,453$ billion.

Step 5 ：For the year 2015, we substitute $y=15$ into the function to get $g(15)=560\ast 15+8853=17253$. So, the GDP in 2015 is about $\mathrm{\$}17,253$ billion.

Step 6 ：Final Answer: The GDP in 2002 is about $\boxed{{\displaystyle 9,973}}$ billion dollars. The GDP in 2010 is about $\boxed{{\displaystyle 14,453}}$ billion dollars. The GDP in 2015 is about $\boxed{{\displaystyle 17,253}}$ billion dollars.