Question

Online jewelry sales have increased steadily. In 2003, sales were approximately 2 billion dollars, and in 2013 they were approximately 5.5 1 billion. Construct a model to predict online jewelery sales. Use your model, to find the predicted online jewelry sales for 2015? (Express your answer rounded correctly to the nearest tenth of a billion.)

Answer 1

1)
`y=2(1+0.081)^x`

2) 6.4 billion.

Explanation:

1) Let the model that is used to find online jewelry sales ( in billions ) after x years,

`y=a(1+r)^x`

Let 2003 is the initial year,

That is, for 2003, x = 0,

The sales on 2003 is 2 billion, y = 2,

⇒
`2=a(1+r)^0\implies a=2`

Now, in 2013 they were approximately 5.5 1 billion

i.e. if x = 13 then y = 5.51,

`\implies 5.51 = a(1+r)^(13)`

`5.51=2(1+r)^(13)`

With help of graphing calculator,

r = 0.081,

Hence, the model that represents the given scenario is,

`y=2(1+0.081)^x`

2) For 2015, x = 15,

Hence, online jewelry sales for 2015 would be,

`y=2(1+0.081)^(15)=6.43302745602\approx 6.4\text{ billion}`