the table lists data regarding the average salaries of several profssional athletes in the years 1991 and2001
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 in 1991 the salry was $1440,000 and in 2001 the salary was $257000 Sx= and the salary in 2005 is and the salary in 2010 will be
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To find a linear function that fits the data, we can use the two given data points: the average salary in 1991 and the average salary in 2001.
Given data points:
- In 1991, the salary was $144,000.
- In 2001, the salary was $257,000.
Let's denote the years as x and the salaries as y. We have two data points: (1991, 144000) and (2001, 257000).
a) Now, we can calculate the slope, m, of the linear function using the formula:
m = (change in y) / (change in x)
= (y2 - y1) / (x2 - x1)
= (257000 - 144000) / (2001 - 1991)
b) Calculation:
= 113000 / 10
= 11300
The calculated slope is 11300.
Next, we can use the point-slope equation of a line to find the equation of the linear function. The point-slope equation is given by:
(y - y1) = m(x - x1)
Let's use one of the data points, (1991, 144000), to write the equation:
(y - 144000) = 11300(x - 1991)
Now, we can simplify the equation:
y - 144000 = 11300x - 22723000
Rearranging the terms, we get:
y = 11300x - 22723000 + 144000
y = 11300x - 22579000
Therefore, the linear function that fits the data is y = 11300x - 22579000.
c) To predict the average salary in 2005 and 2010, we substitute the respective years, 2005 and 2010, into the linear function equation:
For the salary in 2005:
y = 11300(2005) - 22579000
Solving this equation will give you the predicted average salary in 2005.
For the salary in 2010:
y = 11300(2010) - 22579000
Solving this equation will give you the predicted average salary in 2010.