For this problem, we will use desmos.com/calculator to plot the points and find an equation (this is called regression).

The following table is the predicted percentages of the percent of adults diagnosed with diabetes.

make a linear model that fits the table.

Year. Percent

2010. 15.7

2015 18.9

2020. 21.1

2025 24.2

2030. 27.2

2035 29.0

2040. 31.4

2045 32.1

2050. 34.3

a) Let x be the number of years after 2000 and y be the percent of adults with diabetes. What are the ( x, y) points that represent the data in the first three rows of the table, (i.e. what are the first three coordinate points)?

b) Go to https://www.desmos.com/calculator/pqqwugoezn. ( PLEASE USE THIS FOR THE GRAPH )

c) Fill in the table in the website with the data from the table. Keep in mind that x represents the number of years after 2000.

d) Take the values from the online calculator and write the linear model (equation) for the data.Using that model, what year does the model predict that 30% of the adult population will have diabetes? Find the year by hand (you can use a calculator) not from the graph and round your answer to one decimal place.

e) Pick two points from the table. from the two points make a different linear model using these two points by creating the equation of a line. Show as much work and steps as possible.

f) Using your new model, what year does the model predict that 30% of the adult population will have diabetes? Find the year by hand (you can use a calculator) and round your answer to one decimal place.

g) Suppose the quadratic equation below fits the data best.

D(x) =0.00434x2+ 0.726x+ 8.799

Find the year when the percentage of adults with diabetes is predicted to be at a maximum.

work by hand but do not complete the square (you can find the value in another algebraic way).