Question

In 2003, a particular company had 1091 stores and in 2007 there were 1062 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.
No, the number of stores increases as t decreases.
No, the number of stores increases as t increases.
Yes, the number of stores decreases as t decreases.
Yes, the number of stores decreases as t increases.
No, this company will always have stores.

Answer 1

y(t) = -7.25t + 1112.75

2012 stores = 1026

2014 stores = 1011

Yes, the number of stores decreases as t decreases.

Explanation:

2003: (3, 1091)

2007: (7, 1062)

Before doing any calculations, we see that as the years pass, the number of stores decreases. As x increases, y decreases. This is a case of a negative slope.

Now we use the two points above to find a linear equation.

y(t) = mt + b

m = (1062 - 1091)/(7 - 3) = -29/4 = -7.25

y(t) = -7.25t + b

1091 = -7.25 × 3 + b

b = 1112.75

y(t) = -7.25t + 1112.75

For 2012, t = 12:

y(12) = -7.25 × 12 + 1112.75 = 1026

1026 stores in 2012

For 2014, y = 14:

y(14) = -7.25 × 14 + 1112.75 = 1011

1011 stores in 2014

The answers are reasonable since we see the number of stores decrease as t increases.