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3 years ago

Find the equation of the exponential function represented by the table below

Mathematics

1 answer:

Gennadij [26K]3 years ago

4 0

Answer:

y = 3^(1 + x)

Step-by-step explanation:

Notice that each time x increases by 1, y increases by a factor of 3.

Thus, the required equation has the form y = 3^x.

Check: If x = 0, do we get 3? No. Therefore we must modify the exponent:

y = 3^(1 + x)

Check: If x = 0, do we get 3? 3^(1 + 0) = 3 (correct)

If x = 2, do we get 27? 3(1 + 2) = 3^3 + 27 (correct)

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What is the angle of rotation for a point on a circle for drawing a regular 15-gon?

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The answer is 120
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3 years ago

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PLS HELP ASAP! 30 POINTS! functionf(x) is graphed on the coordinate plane.

lorasvet [3.4K]

The function will be given f(x) = -4 ( x -0.5)

<h3 /><h3>What is the equation of a line passing through two points?</h3>

Graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by

$\rm (y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)$

We can see that the line is passing through the points ( 0.5,0) and ( 0,-2). so we will find the function by using the equation of the line passing through two points.

Write an equation for the trend line.

(x₁, y₁) → (0.5,0)

(x₂, y₂) → (0, -2)

Then we have

y - 0 = ( -2 - 0)/( 0 - 0.5)(x - 0.5)

y - 0 = ( -2/-0.5) ( x - 0.5)

y = -4 ( x -0.5)

Learn more about straight-line equations here:

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2 years ago

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

KiRa [710]

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.

6 0

3 years ago

Information about a play took up 1/3 of the pages in the program. Information about the actors took up 1/4 of the remaining page

Lisa [10]

Answer:

Step-by-step explanation:

Comment

Let the number of pages = x

Play = 1/3x

Actors = 1/4(x - 1/3 x)

Actors = 1/4(2/3x)

Actors = 2/12 x

Producer Director etc = 2 pages

Equation

Actors = 2 pages

2/12 x = 2

Solution

2x/12 = 2 Multiply both sides by 12

12*2x/12 = 2*12 Combine

2x = 24 Divide by 2

2x/2 = 24/2 Combine

x = 12

Answer

The program had 12 pages.

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2 years ago

Jack is using a ladder to hang lights up in his house.he places the ladder 5 feet from the base of his house and leans it so it

Yakvenalex [24]

You did not complete your question but I think this is what you are looking for. View the image.

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3 years ago