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In this problem we are given the piecewise function f f of t is equal to 1 when 0 less than or equal to t less than 2 and e raised to negative t minus 2 when t is greater than or equal to 2.
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The first question is to graph this piecewise function f f of t for all t greater than or equal to.
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To 0.
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Now this function takes the value 1 in the interval 0 2 and after that it takes the value e raise to negative of t minus 2 when t is greater than or equal to 2.
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So graph this function this is the graph of the function f of t for all t greater than or equal to 0.
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The next question is to use the unit step function h of t to write f of t as a single function for all t greater than or equal to zero.
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Now the unit step function h of t is defined as 1 when t is greater than or equal to 0 and 0 when t is less than 0.
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Also, h of t minus a is defined as 1 when t is greater than or equal to a and 0 when t is less than a.
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Using the unit step function h of t minus 2, we can write f of t as f of t is equal to 1 plus h of t minus 2 times e raise to negative 1 .000.
01:53
Of t minus 2 minus 1.
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Now see that when t is between 0 and 2 we have h of t minus 2 is 0 therefore f of t is equal to 1 in that interval and when t is greater than or equal to 2, h of t minus 2 is equal to 1...