MATHEMATICS HIGH SCHOOL

In 1990 retail sales at bookstores were about $7.4 billion. In 1997 retail sales at bookstores were about $11.8 billion. Write a linear model for retail sales s (in billions of dollars) at bookstores from 1990 through 1997. Let T represent the number of year since 1990. Then estimate the retail sales at bookstores in 2012.

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Answer 1
Answer:

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= $11.8 + (2012-1997)([$11.8-$7.4][1997-1990])

= $11.8 + 5 ($4.4/7)

= $11.8 4/5 + $22/7

= $59/5 + $22/7

= $413/35 + $110/35

= $523/35 or $14 33/35

answer : SALES IN 2012 WOULD BE $14 33/35 BILLION OR $14.9 3/7
Answer 2
Answer:

Final answer:

A linear model representing retail sales at bookstores from 1990 through 1997 is s(T) = 0.63T + 7.4. The estimated sales at bookstores in 2012 would be approximately $21.46 billion.

Explanation:

To solve this problem, we need to create a linear model. A linear model is a mathematical representation expressed as y = mx + b, where m is the slope, and b is the y-intercept.

To determine the slope (m), we subtract the ending value of retail sales from the starting value and divide by the number of years. So, subtract $7.4 billion (sales in 1990) from $11.8 billion (sales in 1997) and divide by 7 (the number of years from 1990 to 1997): (11.8 - 7.4) / 7 = 0.63. So, m = 0.63.

The y-intercept (b) is the value of y when x = 0. In this model, this corresponds to the sales in 1990, because x is the number of years since 1990, and 'x = 0' therefore corresponds to the year 1990. So, b = $7.4 billion.

The final linear model for retail sales at bookstores from 1990 through 1997 is s(T) = 0.63T + 7.4.

To estimate the retail sales at bookstores in 2012, we plug T = 22 (because 2012 is 22 years after 1990) into our linear model: s(22) = 0.63*22 + 7.4 ≈ $21.46 billion. So, the estimated retail sales in bookstores in 2012 were about $21.46 billion.

Learn more about Linear Models here:

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