A certain company estimates that it can sell f(x)-thousand video game consoles at the price of $x as given in the table. Use a linear approximation to estimate the number of consoles that can be sold at $62.
A) approximately 105 thousand consoles
B) approximately 108 thousand consoles
C) approximately 130 thousand consoles
D) approximately 138 thousand consoles

Question

A certain company estimates that it can sell f(x)-thousand video game consoles at the price of $x as given in the table.  Use a linear approximation to estimate the number of consoles that can be sold at $62.
A) approximately 105 thousand consoles 
B) approximately 108 thousand consoles 
C) approximately 130 thousand consoles 
D) approximately 138 thousand consoles

Quizplus · Accepted Answer

To use linear approximation, we need to find the equation of the line that best fits the given data. We can use the two given points (60, 120) and (64, 96) to find the slope and y-intercept:
slope = (96-120)/(64-60) = -6
y-intercept = 120 - (-6)*60 = 480
So, the equation of the line is given by: f(x) = -6x + 480
Now, we can use this equation to estimate the number of consoles sold at $62:
f(62) = -6*62 + 480 = 108
Therefore, the estimated number of consoles sold at $62 is approximately 108 thousand, which is choice B.

A Certain Company Estimates That It Can Sell F(x)-Thousand Video