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 $g(y)=560 y+8853$, 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 $\$ 9,973$ billion. (b) What value of $y$ corresponds to the year 2010? $y=10$ (Type a whole number.) The GDP in 2010 is about $\$ 14,453$ billion. (c) What value of $y$ corresponds to the year 2015? $y=15$ (Type a whole number.) The GDP in 2015 is about $\$ 18,230$ billion. example Get more help - Clear all Final check
Solution
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 $g(y)=560 y+8853$ to calculate the GDP for each year.
Step 3 ：For the year 2002, we substitute $y=2$ into the function to get $g(2)=560*2+8853=9973$. So, the GDP in 2002 is about $\$ 9,973$ billion.
Step 4 ：For the year 2010, we substitute $y=10$ into the function to get $g(10)=560*10+8853=14453$. So, the GDP in 2010 is about $\$ 14,453$ billion.
Step 5 ：For the year 2015, we substitute $y=15$ into the function to get $g(15)=560*15+8853=17253$. So, the GDP in 2015 is about $\$ 17,253$ billion.
Step 6 ：Final Answer: The GDP in 2002 is about $\boxed{9,973}$ billion dollars. The GDP in 2010 is about $\boxed{14,453}$ billion dollars. The GDP in 2015 is about $\boxed{17,253}$ billion dollars.
