Questions: The table shows projections of sales (in billions of dollars) of hepatitis C treatments for a certain region from 2012 to 2016. Complete parts (a) through (c). Year Sales ( billions) 2012 4.6 2013 4.9 2014 6.6 2015 7.9 2016 9.7 a. What is the quadratic function that best models these sales as a function of the number of years after 2010? Let x represent the number of years after 2010 and y represent the number of billions of dollars in sales of treatments. y=0.186 x^2-0.166 x+4.060 b. Graph the model and the data on the same axes, with x equal to the number of years after 2010. Choose the correct graph below. A. B. c. D.

The table shows projections of sales (in billions of dollars) of hepatitis C treatments for a certain region from 2012 to 2016. Complete parts (a) through (c). Year Sales ( billions) 2012 4.6 2013 4.9 2014 6.6 2015 7.9 2016 9.7 a. What is the quadratic function that best models these sales as a function of the number of years after 2010? Let x represent the number of years after 2010 and y represent the number of billions of dollars in sales of treatments. y=0.186 x^2-0.166 x+4.060 b. Graph the model and the data on the same axes, with x equal to the number of years after 2010. Choose the correct graph below. A. B. c. D.
Transcript text: The table shows projections of sales (in billions of dollars) of hepatitis C treatments for a certain region from 2012 to 2016. Complete parts (a) through (c). Year & Sales ( $\$$ billions) 2012 & 4.6 2013 & 4.9 2014 & 6.6 2015 & 7.9 2016 & 9.7 a. What is the quadratic function that best models these sales as a function of the number of years after 2010? Let x represent the number of years after 2010 and y represent the number of billions of dollars in sales of treatments. \[ y=0.186 x^{2}-0.166 x+4.060 \] b. Graph the model and the data on the same axes, with $x$ equal to the number of years after 2010. Choose the correct graph below. A. B. c. D.
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Solution

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Solution Steps

Step 1: Find the best fit quadratic function

Given the data points representing years after 2010 (x) and sales in billions of dollars (y), the question asks for the best fit quadratic function. It is provided as y = 0.186x² - 0.166x + 4.060.

Step 2: Plot the data points

The data points are (2, 4.6), (3, 4.9), (4, 6.6), (5, 7.9), and (6, 9.7). These points should be plotted on a graph.

Step 3: Graph the quadratic function

The quadratic function y = 0.186x² - 0.166x + 4.060 should be graphed on the same axes as the data points. The correct graph will show the parabola passing close to the plotted data points, visually demonstrating the best fit. Based on the upward concavity of the given equation, and where the vertex will likely fall based on the equation, and the provided graph choices, B is the closest match.

Final Answer: The correct graph is B.

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