WEBVTT
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in this problem, we're going to use a graphing
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calculator to compute an exponential regression for the data given
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in the table. So we go to the stat
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menu and then into edit, and we type our
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numbers into list one and list, too. And
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the numbers I typed into list one represent the number
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of years since the year 1900. So year zero
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is 1900. Year 10 is 1910 etcetera. So
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I didn't type the numbers exactly from the table.
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I subtracted 1900 from each of them. And then
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the numbers in column two are the populations. So
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what we want to do with this is find the
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exponential regression. And it might be interesting also to
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look at the scatter plot and see if it looks
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like exponential growth. So we can go into the
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stat plot menu. We can turn on plot one
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when we can go to zoom and go to zoom
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stat number nine and we can see our scatter plot
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. Okay, so from here, we want to
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go ahead and find the regression equation. So we
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go back to stat over to calculate, and then
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we go down until we find exponential regression is a
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bit farther down in the list. There we go
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. Exponential regression. We pressed. Enter, we're
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using List one and list, too. We do
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want to store the regression equation in our Y equals
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menu. So when you get to this point,
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you press the variables button, go over to why
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variables choose function and choose why one and then we
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can calculate. So if we round these numbers,
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we have approximately y equals 80.8 times, 1.1 to
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the X power. Okay, so if you press
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why equals, you will see that that has now
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been pasted into the y equals and you and we
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can work with it. So what we want to
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do is use this equation to estimate the population in
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1925 and predict the population in the year 2020 which
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just so happens to be the year in which I'm
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talking right now. So what we can do is
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use the table for that. So I'm going to
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go into table set and make sure that my independent
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variable is set to ask, and that will allow
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me to type in my own X values. Once
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that is set, I can go into the table
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, which is second graf and it doesn't matter if
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you have numbers here. You can delete them if
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you want, but it's not going to matter.
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So for the year 1925 we want to type in
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a 25 x, And that tells us 110.82 is
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the population of the United States in millions, according
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to this model from the year 1925. And now
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let's type in the year 1 20 to represent the
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year 2020 and we get 367 million for the population
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in the United States.