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Problem 88 Hard Difficulty

The table shows the average salaries $S$ (in thousands of dollars) for baseball players in Major League Baseball from 2001 through 2012. (Source: CBS Broadcasting, Inc.)
(a) Use a graphing utility to create a scatter plot of the data, where $t$ represents the year, with $t=1$ corresponding to $2001.$
(b) A model that approximates the data is
$S=110.386 t-\frac{16.4988}{t}+2167.7,1 \leq t \leq 12$
Graph the model and the data in the same viewing window. Is the model a good fit for the data?
(c) Use the model to predict the first year in which the average MLB player salary exceeds $\$ 4$ million.

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Top Algebra Educators
Catherine R.

Missouri State University

Heather Z.

Oregon State University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Video Transcript

it is given that the equation s is equal to be 1 10.38 60 minus 16.4988 He went by T plus 2 16 2167.7. Well, the value of tea is greater than or equal to one less than or equal to 12. Where d you present that year and s to present the salary now? No, we need to floated the graph off the given conditions. The graph we'll look like as no, we predict the first year in which the average MLB player celery exceed $4 million. Now put S is equal to four $1,000,000. We get the question four is equal to 110.38 60 minus buying a 16.4988 upon t plus 2 +167 points out number. Simplifying it, we get the quadratic equation. 110.38 60 Scared plus 2 163.70 minus 16.4988 is equal to zero. Now, By comparing this equation with the standard quarter dick equation and using the quadratic formula, we have the value of T is equal to B minus 2163.7 plus minus 2165.38 Do I do to buy 2 to 0.772 which is approximately equal to 1.68 So in so in after one year, 1.5 year, the salary off the player will exceeds $4 billion.

Top Algebra Educators
Catherine R.

Missouri State University

Heather Z.

Oregon State University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University