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the graph below shows the percentage of American adults who smoke over time assuming the trend shown in the data has been consistent since 1945 used the graph to estimate the percentage of American adults who smoked in 1945 so let's see what's going on here the horizontal axis here they say years since 1965 so this point right over here this is zero years since 1965 so this really represents 1965 and we see it looks like around let's see if I were to eyeball it it looks like it's around 42% of Americans just looking at this graph another side of the exact number roughly 41 or 42 percent of Americans smoked in 1965 based on this graph and then five years later this would be 1970 ten years later that would be nineteen nineteen seventy five and they don't they don't sample the data or we don't have data from every given year this is just from some of the years that we happen to have but what it is clear it looks like we have a negative linear relationship right over here that it would not be difficult to fit a line so let me try to do that so I'm just going to eyeball it and try to fit a line to this data so that our line might look something like that so it looks like a pretty strong negative linear relationship when I say it's a negative linear relationship we see that as time increases the percentage of smokers in the US is decreasing so that's what makes it a negative a negative relationship now what are they asking they want us to estimate the percentage of American adults who smoked in 1945 well 1945 would be to the left of zero so we could even think of it as if 1945 is 20 years before 1965 so let me see if I can draw that so 20 years before 1965 let's see this would be five years before 1965 10 years 15 years 20 years before 1965 so I could even put that as negative 20 right over here negative 20 years since 1965 you could view as 20 years before 1965 so that would represent 1945 there and one thing that we could do is very roughly just try to extend to this negative or linear relationship backwards and they allow us to do that by saying assuming the trend shown and the data has been consistent so the trend has been consistent this line represents the trend so let's just keep going backwards keep going backwards at the same rate so something something like that I want to make sure that it looks looks at the same looks like it's the same rate right over here and you could just try to eyeball it you could say will exceed 20 years ago 1945 if I were to extend that line backwards it looks like it looks like there were about 52% of the population was smoking this seems it seems like we're about 52 percent right over here another way to think about it was B to actually try to calculate the rate of decline and let's say we do it over every 20 years because that'll be useful because we're going 20 years back so if we go 20 years from this point so this is 1965 you go 20 years in the future so that is that is 10 years and then that is 20 years so my change in the horizontal is 20 years what's the change in the vertical well it looks like it looks like we have a decrease of a little bit more than 10% looks like it's 11 or 12% decrease so I'll just say minus 11 percent right there let's see if that's consistent if we were to go another 20 years so if we go another 20 years it looks like once again we've gone down by about 10 percent so that looks like roughly 10 percent if we're following the line it should actually be the same number so so let me write it this way it's it's approximately down 10% so that little squiggly line I'm just saying approximately negative 10% every 20 years negative 10% every 20 years so if you go back 20 years so if you go back 20 years you should increase you should increase your percentage by 20 percent so this should go up by or you should increase your printer percent I should say so if we started at 41 or 42 once again this is what we saw when we just eyeballed it you should get to 51 or 52 percent so my estimate of the percentage of American adults who smoked in 1945 would be 51 or 50 52 percent