The table lists data regarding the average salaries of several professional athlethes in the years 1991 and 2001
A) use the data points to find a linear functions that fits the data
Year Salary
1991 $272,000
2001 $1,480,000
B) what would the salary be in 2005 and 2010
To find a linear function that fits the given data, you can use the slope-intercept form of a linear equation, which is y = mx + b. In this case, the "x" variable represents the year, and the "y" variable represents the salary.
A) To find the slope (m) of the linear function, you can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the given data points (1991, $272,000) and (2001, $1,480,000), you can calculate the slope as follows:
m = (1,480,000 - 272,000) / (2001 - 1991)
m = 1,208,000 / 10
m = 120,800
Now, to find the y-intercept (b), you can substitute one of the data points into the equation to find b. Let's use the point (1991, $272,000):
272,000 = 120,800(1991) + b
272,000 = 239,699,200 + b
b = 272,000 - 239,699,200
b = -239,427,200
So the linear function that fits the data is:
Salary = 120,800(year) - 239,427,200
B) To find the salaries in 2005 and 2010, substitute the corresponding years into the linear function.
For 2005:
Salary = 120,800(2005) - 239,427,200
Salary = 241,016,000 - 239,427,200
Salary = $1,588,800
For 2010:
Salary = 120,800(2010) - 239,427,200
Salary = 243,808,000 - 239,427,200
Salary = $4,380,800
So the estimated salaries in 2005 and 2010 would be $1,588,800 and $4,380,800, respectively, according to the linear function.