Trouble with first order system

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JamesGoh
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Im going over some class notes on LTI systems, and attempted a problem involving first order systems.

I have attached the problem, it is on page 1B.2 of the attached pdf (its in italics)

Also, I have attached a word doc showing my hand working

many thanks in advance
 

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take a look at this thread, https://www.physicsforums.com/showthread.php?t=174635 if you want some general stuff about how or why convolution comes about in a LTI system.

secondly, i suggest that you post your equations using LaTeX so we can read them. it's too hard decoding what you're saying for me to put the time into it.
 
Am I making any sense after the change to my original post, do i need to consider editting it so it makes more sense ?
 
sorry, but with limited time and voluntary help, you need to put your question together in a manner that we can simply read it on the page. sometimes LaTeX is not necessary, but, if done right, it sure helps.

i'm using linux, and i can't even read your .doc file. i am not going to go through a great effort just to be able to read what it is you're trying to ask. you have to make that effort to present it to us so that we can read it.

another possibility (but you won't have any tools, like LaTeX) is to post a signal processing question to the USENET newsgroup comp.dsp . then you have to use "ASCII math" notation.