The table lists data regarding the average salaries of several professional athletes in the years 1991 and 2001.
a) Use the data points to find a linear function that fits the data.
b) Use the function to predict the average salary in 2005 and 2010.
$\begin{array}{cc}\text { Year } & \text { Average Salary } \\ 1991 & \$ 266,000 \\ 2001 & \$ 1,370,000\end{array}$
A linear function that fits the data is $S(x)=110400 x+155600$.
(Let $x=$ the number of years since 1990, and let $S=$ the average salary $x$ years from 1990.)
The predicted average salary for 2005 is $\$ \square$.
(Round to the nearest whole number.)
Answer
Therefore, the predicted average salary for 2005 is \(\boxed{\$1,811,600}\).
Step 1 ：Given the data points for the years 1991 and 2001, we can find a linear function that fits the data. Let's denote the year as \(x\) and the average salary as \(S\). The linear function is \(S(x) = 110400x + 155600\), where \(x\) is the number of years since 1990.
Step 2 ：To predict the average salary for 2005, we substitute \(x = 15\) into the function, since 2005 is 15 years from 1990.
Step 3 ：After substituting, we get \(S(15) = 110400*15 + 155600 = 1811600\).
Step 4 ：Therefore, the predicted average salary for 2005 is \(\boxed{\$1,811,600}\).
