Question

In 2003, a particular company had 1088 stores and in 2007 there were 1058 stores. Write a linear equation that gives the number of stores in terms of the year. Let t = 3 represent 2003.

y(t) =



Predict the number of stores for the years 2012 and 2014. (Round your answers to the nearest whole number.)

2012 stores

2014 stores

Are your answers reasonable? Explain.
Yes, the number of stores decreases as t decreases.
No, the number of stores increases as t decreases.
No, this company will always have stores.
Yes, the number of stores decreases as t increases.
No, the number of stores increases as t increases.

Answer 1

The number of stores can be modeled by a linear equation y(t) = -7t + 1088, where t represents the number of years after 2003. The predicted number of stores for 2012 is 1031 and for 2014 is 1017. These answers are reasonable as the number of stores decreases over time.

Step-by-step explanation:

The number of stores can be modeled by a linear equation that gives the number of stores in terms of the year. Let t represent the number of years after 2003. We can use two points on the line to determine the equation. In 2003, t = 0 and there were 1088 stores. In 2007, t = 4 and there were 1058 stores. Using the slope-intercept form of a linear equation y = mx + b, where m is the slope and b is the y-intercept, we can write the equation as follows:

y(t) = -7t + 1088

To predict the number of stores for the years 2012 and 2014, we substitute the values of t into the equation and round the result to the nearest whole number:

For 2012, t = 9 (since t = 0 represents 2003), so y(9) = -7(9) + 1088 = 1031 (rounded to the nearest whole number)

For 2014, t = 11, so y(11) = -7(11) + 1088 = 1017 (rounded to the nearest whole number)

These answers are reasonable because the number of stores is decreasing over time as t increases.