00:01
Okay, so for this question, we are given a data set of years and number of acres per farm in the united states.
00:11
And so what we are asked to do is to first plot the data.
00:17
And then we want to sketch a freehand curve that approximates the data and then use that curve to approximate a a of 40, which is how many acres, or sorry, where a is acres and t is time and years.
00:40
So first what i did, i just typed up our data set, our years, and our number of acres per farm, and i just put that in an excel file and made a quick scatter plot.
00:54
And then i fitted a line, a linear regression line on top of the data.
01:03
And we get this equation up here and our r squared value, which tells us how closely this regression line fits our data.
01:14
So 0 .77 is not the best, but in this case, we are asked to sketch our first.
01:24
Freehand curve to approximate the data.
01:27
So this is probably good enough for our purposes here.
01:32
And so we plotted the data.
01:36
We have a curve that fits it.
01:39
And now we want to approximate a of 40.
01:42
So basically, what's that that's telling us when the acres equal 40, what does the time equal? so what year were the number, where the average number of acres per farm equal to 40? and so basically what we're just going to do, we're going to solve our equation and we're going to plug in 40 for y.
02:08
So our line of best fit right here is, remember, y equals mx plus b is our slope of the line.
02:17
So 3 .56x minus 6 ,653...