Actual and predicted fast-food restaurant sales from 1990 to 2010 are given in the table.

Years Since 1990 t	Fast-Food Restaurant Sales ($ millions) S
0	69,840
2	82,433
4	96,341
6	112,882
8	133,372
10	159,126
12	191,461
14	231,693
16	281,138
18	341,112
20	412,932

(a) Using averages, estimate S(11). $ _________ Explain what the value of the answer means in the real-world context.

Option 1: This means that the amount of food sales in 2001 is estimated as being in the middle of the food sales from 2000 and 2002.

Option 2: This means that the difference between the amount of food in 2000 and in 2001 is the same as the difference between the amount of food in 2001 and in 2002, which is this value in each year.

Option 3: This means that 2000 and 2002 both had the same amount of food sales each year.

Option 4: This means that if 2000 and 2002 both had the same amount of food sales each year it would have been this value in each year.

Option 5: This means that 2001 had the same amount of food sales as 2000 and 2002, which is this value in each year.

(b) Using the average rate of change from t = 0 to t = 10, estimate S(11). $ __________ Explain what the value of the answer means in the real-world context.

Option 1: This means that from 1990 to 2000 if the fast food sales decreased the same amount each year the sales in 2001 would have been 69,840 - 8,928.6(1) = 60,911.4 or $60,911,400,000.

Option 2: This means that from 1990 to 2000 if the fast food sales increased the same amount each year the sales in 2001 would have been 69,840 + 8,928.6(11) = 168,054.6 or $168,054,600,000.

Option 3:This means that from 1990 to 2000 if the fast food sales decreased the same amount each year the sales in 2001 would have been 69,840 + 8,928.6(11) = 168,054.6 or $168,054,600,000.

Option 4: This means that from 2000 to 2010 if the fast food sales increased the same amount each year the sales in 2011 would have been 69,840 + 8,928.6(11) = 168,054.6 or $168,054,600,000.

Option 5: This means that from 1990 to 2000 if the fast food sales increased the same amount each year the sales in 2001 would have been 69,840 + 8,928.6(1) = 78,768.6 or $78,768,600,000.

(c) If you were to estimate S(13), would it be possible to use either averages or the average rate of change to arrive at the estimate? Justify your answer.

Option 1: Yes, but the average and the average rate of change would not represent the same thing or provide the same numerical value.

Option 2: Yes, and average and the average rate of change would represent the same thing or provide the same numerical value.

Option 3: No, neither the average and the average rate of change would represent the value of S(13).

Option 4: You could use the averages, but not the average rate of change to arrive at the estimate.

Option 5: You could use the average rate of change, but not the averages to arrive at the estimate.

(d) Using successive differences, estimate S(22). $ _________ Explain what the value of the answer means in the real-world context.

Option 1: According to the estimation, in the year 2022, fast food restaurant sales will reach this value.

Option 2: The difference in each successive year is this value.

Option 3: According to the estimation, in the year 2012, fast food restaurant sales will reach this value.

Option 4: The rate of change for each year is this value.

Option 5: According to the estimation, in the year 2002, fast food restaurant sales will reach this value.