Explain in detail how the answers were determined for critical thinking questions.

able 1: Selected CPUs with corresponding speed ratings in MIPS.

Processor	Year	t Years After 1974 When Introduced	Million Instructions per Second (MIPS)
1	1974	0	0.29
2	1978	4	0.33
3	1979	5	0.75
4	1982	8	1.28
5	1985	11	2.15
6	1989	15	8.7
7	1992	18	25.6
8	1994	20	188
9	1996	22	541
10	1999	25	2,064
11	2003	29	9,726
12	2006	32	27,079
13	2008	34	59,455

(Instructions per second, n.d.)

This information can be mathematically modeled by the exponential function:

Be sure to show your work details for all calculations and explain in detail how the answers were determined for critical thinking questions. Round all value answers to three decimals.

Generate a graph of this function, , years after 1974, using Excel or another graphing utility. (There are free downloadable programs like Graph 4.4.2 or Mathematics 4.0; or, there are also online utilities such as this site and many others.) Insert the graph into your Word document that contains all of your work details and answers. Be sure to label and number the axes appropriately. (Note: Some graphing utilities require that the independent variable must be “x” instead of “t”.)

Find the derivative of with respect to .

Choose a -value between 20 and 34. Calculate the value of

Interpret the meaning of the derivative value that you just calculated from part 3 in terms of the function.

If the function is reasonably accurate, for what value of will the rate of increase in MIPS per year reach 1,000,000 ? Approximately which year does that correspond to?

For the -value you chose in part 3 above, find the equation of the tangent line to the graph of at that value of . What information about the function can be obtained from the tangent line?

Using Web or Library resources research to find the years of introduction and the processor speeds for both the CPU A and the CPU B. Be sure to cite your creditable resources for these answers. Convert the years introduced to correct values of and determine how well the function predicts when these CPUs’ processor speeds occurred.