Question

In 2003, online holiday sales were $17 billion, and in 2006, they were $26 billion.

(a) Find a linear function S that models these data, where x is the year.
(b) Interpret the slope of the graph of S.
(c) Predict when online holiday sales might reach $41 billion.

Answer 1

(a)
point A (2003, 17)
point B (2006, 26)

\[slope = { {\Delta y} \over { \Delta x } } = { { 26 - 17 } \over { 2006 - 2003 } } = { 9 \over 3 } = 3\]

\[s(x)= ax + b\]
Now substitute slope and 1 point to find b
\[26 = 3 \times 2006 + b \implies b = 26 - 6018 = -5992\]
\[s(x) = 3x -5992\]

(b)
The slope is the amount (in billions) with which the holiday sales increase each year

(c)
\[41 = 3x - 5992 \implies x = 2011\]

Answer 2

Thank you so much sir, very well done!