Respuesta :
Answer: (i) The unit rate at which online jewelry sales have been increasing is 1.33 billion dollars per year.
(ii) The online jewelry sales in 2019 will be 191.7 billion dollars.
Step-by-step explanation:
In 2003, sales were approximately 2 billion dollars and in 2010, they were approximately 14.8 billion dollars.
(i) If [tex]x[/tex] is the number of years after 2003 and [tex]y[/tex] is the amount of sales....
then the equation will be: [tex]y= ab^x[/tex] , where [tex]a[/tex] is the initial amount and [tex]b[/tex] is the growth rate.
for 2003, [tex]x=0[/tex] and for 2010, [tex]x=7[/tex]
So, the two points in form of (x, y) will be: [tex](0,2)[/tex] and [tex](7,14.8)[/tex]
Now plugging these two points int the above equation....
[tex]2= ab^0\\ \\ a= 2\\ \\ and\\ \\ 14.8=ab^7\\ \\ 14.8=2*b^7\\ \\ b^7=7.4\\ \\b= \sqrt[7]{7.4}=1.3309.... \approx 1.33[/tex]
Thus, the online jewelry sales have been increasing at a rate of 1.33 billion dollars per year.
(ii) As we got [tex]a=2[/tex] and [tex]b=1.33[/tex], so the equation will be now: [tex]y= 2(1.33)^x[/tex]
For the year 2019, the value of [tex]x[/tex] will be: (2019-2003) = 16
So plugging [tex]x=16[/tex] into the above equation, we will get.....
[tex]y=2(1.33)^16\\ \\ y=191.7150... \approx 191.7[/tex]
(Rounded to the nearest tenth)
Thus, the online jewelry sales in 2019 will be 191.7 billion dollars.
