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Allushta [10]
3 years ago
11

Online jewelry sales have increased steadily over the last 10 years. In 2003, sales were approximately 2 billion dollars, and in

2010 they were approximately 14.8 billion. (i) Find the unit rate at which online jewelry sales have been increasing. (Express your answer rounded correctly to the nearest hundredth of a billion per year.) billion dollars per year (ii) Construct a model to predict online jewelery sales. According to your model, what should the online jewelery sales be in 2019? (Express your answer rounded correctly to the nearest tenth of a billion.) billion dollars
Mathematics
1 answer:
KiRa [710]3 years ago
6 0

Answer:   <em>(i)  The unit rate at which online jewelry sales have been increasing is 1.33 billion dollars per year. </em>

<em>(ii)  The online jewelry sales in 2019 will be 191.7 billion dollars.</em>

Step-by-step explanation:

In 2003, sales were approximately 2 billion dollars and in 2010, they were approximately 14.8 billion dollars.

(i)  If x is the number of years after 2003 and y is the amount of sales....

then the equation will be:   y= ab^x , where a is the initial amount and b is the growth rate.

for 2003,  x=0 and for 2010,  x=7

So, the two points in form of (x, y) will be:   (0,2) and (7,14.8)

Now plugging these two points int the above equation....

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

Thus, the online jewelry sales have been increasing at a rate of 1.33 billion dollars per year.

(ii)   As we got a=2 and b=1.33, so the equation will be now:  y= 2(1.33)^x

<u>For the year 2019, the value of</u>  x will be: (2019-2003) = 16

So plugging x=16 into the above equation, we will get.....

y=2(1.33)^16\\ \\ y=191.7150... \approx 191.7

<em>(Rounded to the nearest tenth)</em>

Thus, the online jewelry sales in 2019 will be 191.7 billion dollars.


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2 years ago
1. Kyle and John are twins who decided to plan an imaginary trip that started with cliff jumping. There were two different spots
Vikki [24]

Answer:

a) Δx = -35ft

b) Δx = -25ft

c) Kyle traveled 10ft more than John

Step-by-step explanation:

We define a coordinate reference system() in which y = 0 corresponds to the water surface.

a) The initial position of Kyle in our coordinate reference system is:

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   Δx = x_{f} - x_{o} = -15 - 20 = -35 ft

b) The initial position of John in our coordinate reference system is:

   x_{o} = 15 ft

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6 0
3 years ago
(08.07 HC)
andreev551 [17]

Answer:

\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}

\textsf{B)} \quad \left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)

C)  See attachment.

Step-by-step explanation:

Given function:

f(x)=2x^2-x-10

<h3><u>Part A</u></h3>

To factor a <u>quadratic</u> in the form  ax^2+bx+c<em> , </em>find two numbers that multiply to ac and sum to b :

\implies ac=2 \cdot -10=-20

\implies b=-1

Therefore, the two numbers are -5 and 4.

Rewrite b as the sum of these two numbers:

\implies f(x)=2x^2-5x+4x-10

Factor the first two terms and the last two terms separately:

\implies f(x)=x(2x-5)+2(2x-5)

Factor out the common term  (2x - 5):

\implies f(x)=(x+2)(2x-5)

The x-intercepts are when the curve crosses the x-axis, so when y = 0:

\implies (x+2)(2x-5)=0

Therefore:

\implies (x+2)=0 \implies x=-2

\implies (2x-5)=0 \implies x=\dfrac{5}{2}

So the x-intercepts are:

x=-2, \:\:x=\dfrac{5}{2}

<h3><u>Part B</u></h3>

The x-value of the vertex is:

\implies x=\dfrac{-b}{2a}

Therefore, the x-value of the vertex of the given function is:

\implies x=\dfrac{-(-1)}{2(2)}=\dfrac{1}{4}

To find the y-value of the vertex, substitute the found value of x into the function:

\implies f\left(\dfrac{1}{4}\right)=2\left(\dfrac{1}{4}\right)^2-\left(\dfrac{1}{4}\right)-10=-\dfrac{81}{8}

Therefore, the vertex of the function is:

\left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)

<h3><u>Part C</u></h3>

Plot the x-intercepts found in Part A.

Plot the vertex found in Part B.

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The axis of symmetry is the <u>x-value</u> of the <u>vertex</u>.  Draw a line at x = ¹/₄ and use this to ensure the drawing of the parabola is <u>symmetrical</u>.

Draw a upwards opening parabola that has a minimum point at the vertex and that passes through the x-intercepts (see attachment).

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