Write the equation L(x) of a linear function that "fits" the data in your Scatter Diagram as closely as possible. ? In other words, choose two (x,y) data pairs so that a line passing through those two pairs comes as close to the overall data set as possible. ? Write the equation of a line passing through the two (x,y) data pairs you chose. Be sure to show all your work. ? Do not just get the equation from software. Find the equation "by hand."c) Evaluate the limit of your linear model L(x) as x approaches 50% numerically. Be sure to show a table of values and make a clear conclusion about the value of the limit based on the table. d) Evaluate the limit of your linear model L(x) as x approaches 50% algebraically. e) By comparing your work in parts c & d to the original table of data, how accurate is your linear function? Explain briefly. f) Use the Precise Definition of a Limit (delta-epsilon, Section 2.4) to prove the value of your limit from part "d." g) Using the original table of data, find the rate of change (slope) between Indiana and Tennessee. h) Using your linear model, use the limit definition of the derivative from Section 2.7 to find L'(50). i) Explain what your answer to part "h" means and how accurate it is by comparing it to part "g"

1. The following information comes from the Mayo Clinic Tracker and the g Covid Tracker as of December 8, 2021: vaccinated (X) people (Y) m [MEI MEI _EIE- a) Using the data above, create a Scatter Diagram of the data. 0 Plot the pairs in the x/y coordinate plane. 0 Be sure to scale each axis consistently. - Be sure to label what each axis is measuring, in words