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## Precalculus

1. Research and define the concepts of maximum theoretical throughput, channel capacity, and bandwidth. Next, explain the difference between CAT5e and CAT6 Ethernet cables. What specific speeds can each of these cables handle? Listing credible cited resources, please answer these

1. In the table below, based on the first letter of your last name, please select one number from each of the ranges in the x and y columns.

Table A: Estimates of bit-transmissions and times

 First Letter of Your last Name Seconds Gigabits (Gb) A – D 2 to 3.99 2 to 3.99 E – H 4 to 7.99 4 to 7.99 I – L 8 to 15.99 8 to 15.99 M – P 16 to 31.99 16 to 31.99 Q – T 32 to 63.99 32 to 63.99 U – Z 64 to 79.99 64 to 79.99

Given that the throughput is the table’s Gigabits per seconds (Gbps), calculate and record this transfer rate for your chosen values with the formula:

1. Your school’s maximum network bandwidth is 1 Gbps. Does your answer from above exceed that or not? Based strictly on your value, do you think the maximum bandwidth should be raised? Will the network infrastructure need to be upgraded to support CAT6 cables? How did you arrive at this conclusion? Include the factors that influenced your decision.
1. According to your research, the school’s throughput speed R(t) in Gbps, with respect to time in seconds, is best modeled with the rational function:

Generate a graph of this function 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 the Word document containing your answers and work details. Be sure to label and number the axes appropriately.

### 5.      Peak Measured Throughput (PT): Peak or instantaneous throughputs (PT) measure values useful for systems that rely on bursts of data in a CAT5e cable. Unlike continuous streaming, information travels in short bursts. For example, during in-class demonstrations, a computer lab’s user experiences high traffic usage spikes on a very high-bandwidth that is transmitted over a relatively short period of time. Activity is important during these in-use peak times. Peak rates are measured limits taken with respect to throughput as time approaches zero. So for the above function, use algebraic techniques to find:

Based strictly on this result, do you think your school should raise its current network’s bandwidth of 1 Gbps? How did you arrive at this conclusion?

### 6.         Maximum Sustained Throughput (ST): One of the most accurate indicators of system performance for high duty cycle networks is the maximum sustained throughput (ST) averaged over a long period of time. This value measures the network capacity fully utilized over its entire existence. Essentially, high volumes of continuously streamed transmissions max out the amounts of data being transferred in because the network is busy processing current data and unable to efficiently enter the cable. This builds up the delivery time causing latency instabilities. In this case, sustained rates are measured limits taken with respect to throughput as time increases towards infinity. So for the above function, use algebraic techniques to find the following:

Based strictly on this result, do you think your school should raise its current network’s bandwidth of 1 Gbps? How did you arrive at this conclusion?

1. Based on all of your previous results, do you think your school should raise its current network’s bandwidth of 1 Gbps? How did you arrive at this conclusion?

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