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12x L2a MP2 Part 1: Intermediate Algebra - Computing Average Rate of Change (Part 1) - YouTube
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in this example we're going to be
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looking at a concept called average rate
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of change average rate of change for a
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specified interval is the ratio change
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in output over change in input let's see
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how that works with this problem the
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function e of T equals three thousand
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eight hundred sixty one minus seventy
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seven point two times T gives the
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surface elevation in feet above sea
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level of Lake Powell
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two years after 1999 use the function
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and your graphing calculator to complete
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the table below so let's enter this
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function into our graphing calculator
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we're going to go to our y equals and if
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there's anything in there let's clear it
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out I'm going to enter three eight six
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one minus seventy seven point two and we
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can't do t but we can do X so there is
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our function what I want to do is access
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the table but before I do that I want to
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go to table set that's that's blue so
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I'm going to do second table set I want
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to be sure that my table starts at zero
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my table starts at six so I'm going to
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change that to zero also I want to be
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sure that my change in table values
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that's Delta table equals one and that
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both independent and dependent are Auto
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once I have those settings I want to go
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to my table and I should be able to just
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read the values off of the table right
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on to my written table here so this was
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in 1999
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that's your zero the surface elevation
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was 3861 feet the next year in 2000 it
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was three thousand seven hundred eighty
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three point eight
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feet so I'm just going to keep going
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down here and writing in all the
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information so check your table and be
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sure that yours looks like mine notice
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there is the skip here from three to
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five so your years go from 2002 to 2004
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so be sure that you have the correct
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data written down for the outputs for T
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equals three and T equals five so let's
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use this information to help us respond
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to Parts A B and C first part a so
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determine the average rate of change of
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the surface elevation between 1999 and
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2000 so we're going to be working with
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these two inputs and these two outputs
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to compute the change in output I'm
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going to compute three thousand seven
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hundred and eighty three point eight
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minus three thousand eight hundred sixty
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one divided by one minus zero if I
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perform that subtraction I get negative
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seventy seven point two and the units
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are the units always of the output which
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is feet over the input which is years
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for 2002-2004 we're going to be looking
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at here to here so here to here so
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that's three thousand four hundred
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seventy five minus three thousand seven
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hundred eighty three point eight divided
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by five minus one that's going to give
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us negative three hundred and eight
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point eight over four which is negative
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seventy seven point two feet per year
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and for Part C to determine the average
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rate of change between 2001 and 2005
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2001 is here 2005 is here so I'm using
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these values three three nine seven
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point eight minus three seven oh six
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point six over six minus two we get the
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same thing as we did here and end up
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with negative seventy seven point two
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feet per year
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