Question

The Century of Flight mural measures 28,800 square feet – approximately the size of three football fields. The tables gives data on the rate of which the mural was painted. How many months did it take to finish the mural? Approximate the relationship between the time in months and amount completed with a line of best fit. Express your answer in point-slope form. How many months did it take to complete 14,400 square ft? After 9 months, approximately how many square feet were completed?

Painting The Century of Flight
Months of Work	Amount Completed (ft2)
2	5,236
5	13,091
7	18,327

Answer 1

Let the line of best fit be y = a x + b

The given table is:

Painting	The Century of Flight
Months of Work (x)	Amount Completed (ft2) (y)	x2	xy
2	5,236	4	10472
5	13,091	25	65455
7	18,327	49	128289
​ x = 14	​ y = 36654	​ x2 = 78	​ xy = 204216

Now, the normal equations are:

Substituting the values from the table in equation (1) and (2), we get

Solving equations (3) and (4), we get

Hence, the best fit line is

In point-slope form it can be written as

The number of months required to paint the mural is

The number of months required to paint the 14,400 square feet is

After 9 months, area painted is