Career Planning—Computer Engineers: A profession that has seen a rise and fall recently is...

Career Planning—Computer Engineers: A profession that has seen a rise and fall recently is computer systems engineering. Some see the change resulting in reduced quality of computer software design. “For example, rarely is the processor the bottleneck, but so many people look to ‘tight loops’ to speed up performance when it’s often an I/O issue,” said project management professional Bernard Hayes. (Source: Computerworld.) The number of computer systems engineers employed from 2004 to 2008 can be modeled by the quadratic function

 f(x) = −7.85x2 + 97.05x − 206.6 4 ≤ x ≤ 8

where x represents the number of years since 2000 and f(x) represents the number of computer systems engineers employed, measured in thousands. (Source: National Science Foundation.)

(a) By inspecting the function, is the graph of f concave up or concave down? Explain how you determine your answer.

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(b) Complete Table R.2.

Table R.2

x	f(x)
4
5
6
7
8

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(c) Evaluate and interpret f(5).

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(d) According to the table, during what year was the greatest number of computer systems engineers employed?

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(e) Determine the coordinates of the vertex and round the x-coordinate to the nearest whole number. Is the result the same as in part (d)?

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(f) Determine msec for x = 4 and Δx = 3. Interpret the result.