Question

Online jewelry sales have increased steadily. In 2003, sales were approximately 2 billion dollars, and in 2013 they were approximately 5.64 billion. Construct a model to predict online jewelery sales. Use your model, to find the predicted online jewelry sales for 2015?

Answer 1

Answer:

$S=0.364t+2$

The predicted sales are 7.46 billion dollars

Step-by-step explanation:

Function Modeling

We are given two points that represent the Online jewelry sales. The two points are ( 2003 , 2 ) and ( 2013 , 5.64 ). The second coordinate is expressed in billion dollars. To better represent the function, let's count the time not in absolute years, but in years after 2003. The points now are ( 0 , 2 ) and ( 10 , 5.64 ).

The function to represent the sales (S) will be a line, which general equation is

$\displaystyle S-S_o=\frac{S_1-S_0}{t_1-t_o}(t-t_o)$

Plugging in the points

$\displaystyle S-2=\frac{5.64-2}{10-0}(t-0)$

Operating and rearranging

$S=0.364t+2$

Now we use the model to predict the online sales for 2015, or t=15

$S=0.364(15)+2=7.46$

The predicted sales are 7.46 billion dollars