04.03 HC)
Given the function f(x) = 2(3)x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.

Part A: Find the average rate of change of each section. (4 points)
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)

(10 points)

Answers

Answer 1

Part A:

To find the average rate of change, let us first write out the equation to find it.

Δy/Δx = average rate of change.  

Finding average rate of change for Section A

Δy = f(1) - f(0) = 2(3)^1 - 2(3)^0 = 6 - 1 = 5

Δx = 1- 0 = 1

Plug the numbers in: Δy/Δx = 5/1 = 5

Therefore, the average rate of change for Section A is 5.  

Finding average rate of change for Section B

Δy = f(3) - f(2) = 2(3)^3 - 2(3)^2 = 2(27) - 2(9) = 54 - 18 = 36

Δx = 3 - 2 = 1

Plug the numbers in: Δy/Δx = 36/1 = 36

Therefore, the average rate of change for Section B is 36.  

Part B:

(a) How many times greater is the average rate of change of Section B than Section A?

If Section B is on the interval [2,3] and Section A is on the interval [0,1].  

For the function f(x) = 2(3)^x, the average rate of change of Section B is 7.2 times greater than the average rate of change of Section A.  

(b) Explain why one rate of change is greater than the other.  

Since f(x) = 2(3)^x is an exponential function the y values do not increase linearly, instead increase exponentially. In an interval with smaller x values the rate of change is lower than an interval with larger x values.


Related Questions

two functions are shown below.
f(x)=4^x-62
g(x)=x^2-2x+5

evaluate g(-2)+f(3)

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Answer:

...

Step-by-step explanation:

please i need help with this

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Answer:

1.) Smith

2.) Johnson

Answer:

Step-by-step explanation:

THE LENTH OF A RECTANGLE IS 6 CM AND ITS AREA IS (6XPLUS18) SQUARCM WRITE A EXPPRESIONFOR THE WIDTH

Answers

[tex]\textit{area of a rectangle}\\\\ A=Lw ~\begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=\stackrel{cm}{6}\\ A=\stackrel{cm^2}{6x+18} \end{cases}\implies 6x+18=6w \\\\\\ \cfrac{6x+18}{6}=w\implies \cfrac{6x}{6}+\cfrac{18}{6}=w\implies x+3=w[/tex]

Which decimal is less than 0.12 and greater than 0.008?

Answers

Answer:

Too many examples.

You can pick a number between 120 and 8, then. take that number and move the decimal point to the left 3 spaces.

Here are some examples between 0.12 and 0.008:

0.10.0650.580.07830.119

HELP

please help me!! will mark whoever gets it right brainlist
(question is in image below) ⬇️

Answers

Answer:

[tex](x-6)^2=8[/tex]

Step-by-step explanation:

[tex]x^2-12x+32=4[/tex]

[tex]x^2-12x+32+4=4+4[/tex]

[tex]x^2-12x+36=8[/tex]

[tex](x-6)^2=8[/tex]

Basically, you need to add a number to both sides so that you can reduce the left side to a square. In this case, you add 4.

What is the solution for x in the equation
-4+5x-7=Okay 0+3x-2x

Answers

Answer:

X = 2.75 or 2 3/4 in fraction form

Step-by-step explanation:

We know that the variable X has to make both equations equal.

It is really just crossing out the options.

2.75 can fit in the X variable because if 2.75 was in both equations, the answer would be the same.

So the answer is 2.75

Hope this helps! :)

૮ ・ﻌ・ა

solve the inequality 2x+2-6x<32

Answers

x>−15/2

15/2 is a fraction

Three times the sum of a number and 7 is equivalent to 57.

Answers

Answer:

3(x+7)=57

Step-by-step explanation:

3 is being multiplied by "the sum of a number(or x) and 7". So, we write it as 3(x+7). That is equal to 57, so that makes the expression 3(x+7)=57.

-hope it helps

Equivalent expressions are expressions that have the same values.

The expression is [tex]3(x + 7) = 57[/tex] and the number is 12

Represent the number with x.

So, the sum of a number (x) and 7 would be represented as: x + 7

Three times the sum would be represented as: 3(x + 7)

This expression is equivalent to 57.

So, we have:

[tex]3(x + 7) = 57[/tex]

Divide both sides of the equation by 57

[tex]x + 7 = 19[/tex]

Subtract 7 from both sides of the equation

[tex]x + 7 - 7 = 19 - 7[/tex]

[tex]x = 12[/tex]

Hence, the number is 12

Read more about equivalent expressions at:

https://brainly.com/question/2972832

plot (-7,0) on a graph

Answers

Answer:

To go to (-7,0) on a graph on the x axis go to the left 7 times and plot your point

Step-by-step explanation:

[tex] \: \: \: \: [/tex]

To plot (−7,0) , start at the origin (0,0) and move left 7 units and up 0 units. To plot (7,0) , start at the origin (0,0) and move right 7 units and up 0 units.

hope it helps

Pleaseeeeeeeeeee help me

Answers

Answer:

[tex]\huge\boxed{6x-7y=21}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

[tex]m[/tex] - slope

[tex]b[/tex] - y-intercept (0, b)

We have:

[tex]y=\dfrac{2}{3}x-3\to m=\dfrac{2}{3};\ b=-3[/tex]

From answers:

[tex]6x-7y=21\qquad|-6x\\\\-7y=-6x+21\qquad|:(-7)\\\\y=\dfrac{6}{7}x-3\to m=\dfrac{6}{7};\ \boxed{b=-3}[/tex]

[tex]-\dfrac{2}{3}x+3y=6\qquad|+\dfrac{2}{3}x\\\\3y=\dfrac{2}{3}x+6\qquad|:3\\\\y=\dfrac{2}{9}x+2\to m=\dfrac{2}{9};\ b=2[/tex]

[tex]\dfrac{2}{3}x+3y=-3\qquad|-\dfrac{2}{3}x\\\\3y=-\dfrac{2}{3}x-3\qquad|:3\\\\y=-\dfrac{2}{9}x-1\to m=-\dfrac{2}{9};\ b=-1[/tex]

[tex]x+4y=12\qquad|-x\\\\4y=-x+12\qquad|:4\\\\y=-\dfrac{1}{4}x+3\to m=-\dfrac{1}{4};\ b=3[/tex]

Answer:

6x-7y=21

Step-by-step explanation: :)

what is the value of the 6 in 26,249?

Answers

Answer:

what is the value of the 6 in 26,249?

answer:321305

Step-by-step explanation:

The ratio of the measures of the angles in a
triangle is 4:7:9. Find the measures of the
angles.
x=
The largest angle=

Answers

Explanation:-

We have given measure of angles of the triangle are in ratio 4 : 7 : 9 and here we need to find the measure of largest angle of a ∆.

Let, the three angles of a triangle be 4x, 7x, 9x.

We know that, Sum of all angles of a triangle is 180°.

4x + 7x + 9x = 180°

⇛20x = 180°

⇛x = 180°:20

⇛x = 9°

Now, finding largest angle by putting the value of “x”

4x = 4(9) = 36°7x = 7(9) = 63°9x = 9(9) = 81°

Hence ,the measure of largest angle is 81°.

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The ratio of the measures of the angles of a triangle is 4:6:8. Find the measure of the largest angle. Largest angle?....

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Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-3, 1) and point (4, 2) rounded to the nearest tenth?

Answers

Answer:

√(4 - ( - 3))^2 + (2 - 1)^2

√(4 + 3)^2 + (2 - 1)^2

√49 + 1

√50

7.07 = 7.1 units

find the mean of 90 100 100​

Answers

Answer: 100

Step-by-step explanation:

[tex]\frac{90+100+110}{3}=\boxed{100}[/tex]

can someone please tell me whether the answer is a, or b? or if it’s none of those. ty :)

Answers

The answer is b y=3x+1

isha's art club has $250. They sell 6 paintings for $16 each. They buy 9 sketchbooks that cost $13 each. Aisha says they now have about $280. Is Aisha’s estimate reasonable? Aisha’s estimate is not reasonable. They earned about $120 and spent about $120 so they should have the same amount of money as they started with. Aisha’s estimate is not reasonable. They earned about $100 and spent about $120 so they should have about $20 less than they started with. Aisha’s estimate is reasonable. They earned about $100 and spent about $130 so they should have about $30 more than they started with. Aisha’s answer is reasonable. They earned about $60 and spent about $90 so they should have about $30 less than they started with.

Answers

Answer:

Step-by-step explanation:

Aisha’s estimate is not reasonable.

They earned about $100 and spent about $120 so they should have about $20 less than they started with.

The heights of NFL football players are approximately normally distributed with a mean of 71.5 inches and a standard deviation of 2.3 inches. The middle 75% of all NFL players have heights between
(A) 68.9 inches to 76.1 inches
(B) 69.2 inches to 73.8 inches
(C) 68.9 inches to 74.1 inches
(D) 66.9 inches to 76.1 inches
(E) None of the above give an accurate interval

Answers

Answer:

I would say B

Step-by-step explanation:

I'm sorry, I don't have an explanation

The middle 75% of all NFL players have heights between in (A) 68.9 inches to 76.1 inches.

What is Standard score?

It is the representation of a data value in terms of distance from standard deviation from the mean. It is also called z-score.

It measures how many standard deviations the measure is from the mean. After finding the z-score, we have to look at the z-score table and then the p-value associated with this z-score, which is the percentile of X.

Given that Mean = μ = 64.4 inches

Standard Deviation = σ = 2.3 inches

We have to find the standard score for players height;

So, Let x = 75% = 0.75

Therefore the formula for z-score is:

x - mean / S.D

0.75 = x - 71.5/2.3

x = 76.10

Rounding off to nearest hundredth

z-score = 76.1

Hence, The middle 75% of all NFL players have heights between in

(A) 68.9 inches to 76.1 inches.

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#SPJ2

Function 1 is defined by the equation y=-1/4r-5

Answers

Step-by-step explanation:

and what is function 2 ?

but I think I can risk a guess based on the little piece of the graph I can see.

the y-intercept is simply the point on the y-axis (that means x=0), where the line crosses.

in other words, it is the y-value when x = 0.

the y-intercept of function 1 is therefore -5.

and the picture suggests that the visible line would cross the y-axis at about y=-6.

as -5 is greater than -6, function 1 has the greater y-intercept.


In Manhattan, there are 15 CoffeeStops per 100,000 people Manhattan has approximately 1,602,000 people How many Coffee Stops are there?

Answers

Answer:

Given that 15coffee stops=100,000people

then: x= 1,602,000

100,000×x= 15×1,602,000

100,000x= 24,030,000

100,000x÷100,000= 24,030,000÷100,000

x= 240.3

so therefore there are 240.3 coffee stops if there are 1,602,000

Manhattan has approximately 1,602,000 people. Then the number of coffee shops will be 241.

What are ratio and proportion?

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

In Manhattan, there are 15 CoffeeStops per 100,000 people.

Then the number of coffee shops per person will be

⇒ 15 / 100,000

⇒ 1.5 × 10⁻⁴ coffee shops per person

Manhattan has approximately 1,602,000 people.

Then the number of coffee shops will be

⇒ 1,602,000 × 1.5 × 10⁻⁴

⇒240.3 or 241 coffee shops

Manhattan has approximately 1,602,000 people. Then the number of coffee shops will be 241.

More about the ratio and the proportion link is given below.

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A tennis player makes a successful first serve 49% of the time. If she serves 6 times, what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others.

Answers

Answer: the naswer is 0.154

Step-by-step explanation:

find the x and y intercepts of the following linear function and draw the graph: 2x-8y=-18

Answers

Answer:

Step-by-step explanation:

2x - 8y = - 18

    - 8y = - 2x - 18

         y = ¼x + 2¼

y intercept occurs when x = 0, so b = 2¼  (0, 2¼)

x intercept occurs when y = 0

0 = ¼x + 2¼

¼x = - 2¼

  x = -9     (-9, 0)  

Victor buys5/8 kg of prawns each week. How many kilograms of prawns does he buy in 4 weeks?

Answers

Answer:

37/8

Step-by-step explanation:

5/8+32/8

5+32/8

37/8

PLEASE HELP I WILL GIVE BRAINLEST AND 20 POINTS PLEASEEEE

Answers

Answer:

Question 4: Which equation is parallel to the above equation and passes through the point (35, 30)

[tex]y=[/tex] [tex]\frac{5}{7} x + 5[/tex]  is the correct answer, I found this by inputting the x and y value of the coordinate (35, 30) onto the equation and solving for y-intercept since the slope of all equations is the same (since it's traveling parallel)

[tex]30 = \frac{5}{7} (35) + y\\30 = 25 + y\\5 = y[/tex]

so the equation would be [tex]y=[/tex] [tex]\frac{5}{7} x + 5[/tex]

Question 5: Which equation is perpendicular to the above equation and passes through the point (35, 30)

[tex]y=\frac{-7}{5} x+79[/tex] is the correct answer, I found this using the same method as before, input coordinate values into the equation and solve for the y-intercept (The only thing changed from the last answer is the opposite reciprocal slope).

[tex]30 = \frac{-7}{5}(35) + y \\30 = -49 + y \\79 = y[/tex]

so the equation would be [tex]y=\frac{-7}{5} x+79[/tex]

pythagorean theorem to find the length of the hypotenuse in the triangle 16 30

Answers

Answer:

the answer is 34.

Step-by-step explanation:

When will Road to a killcam 100 come out?

Answers

Answer:T he first season of Black Ops Cold War has been underway for almost a month now. The game has been having great success since it released back in November. One aspect of the multiplayer that a lot of players were disappointed with, was the lack of a final killcam.

Step-by-step explanation:

Answer:

The final Killcam is a Call of Duty staple. Every player in the game can see who got the final elimination of the game, and how they did it. The randomness is part of the fun; sometimes you’ll see an insane 360 Tomahawk kill, or you can have a good laugh at someone missing all of their shots before finally getting the elimination.

However, Black Ops Cold War has opted for a ‘Best Play’ system. Most of the time, you’ll see someone get a multi-kill from some point in the match. While you do often see impressive plays, the fun randomness element is mostly taken out and this has had a negative impact on Search and Destroy.

A Treyarch developer has now confirmed that they will be adding the final Killcam system to Cold War’s S&D in the future.

solve the equation 5-x=8

Answers

Answer:

x = -3

Step-by-step explanation:

1. 5 - x = 8

2.   +x    +x

3. 5 = x + 8

4. -8       -8

5. x = -3

Rearrange the terms
5 - x = 8
-x + 5 = 8


Subtract 5 from both sides
-x + 5 = 8
-x+5-5 = 8-5

subtract the numbers ( simplify )
-x = 3


divide both sides
-x = 3
-x/-1 = 3/-1


simplify
x = 3/-1
x = -3





So therefore, your answer is x = -3

Find the probability of rolling a die twice, first getting a 3 and then an odd number.
(This sounds simple but every answer I get isn’t the correct one)
PLEASE I DON’T UNDERSTAND

Answers

Answer: 1/3 or 0.333333333

Step-by-step explanation:

Probability of getting a 3 is 1/6.

1/6

Probability of getting an odd number is 3/6.

3/6

Multiply them.

1/6*3/6 = 4/12

Simplify.

4/12 = 1/3

Correct me if I am incorrect.

Find the area of a rectangle that is 7 cm long and 3 cm wide. You can use the tool to help you solve.

Answers

Answer:

21

Step-by-step explanation:

The answer is 21 because for finding the area you have to multiply, 7 and 3.

Multiply 7 and 3 you get 21.

Hope this helps :)

Answer:

21

area is equal to length X height. 7 X 3 = 21

Which sentence is punctuated correctly? Finally Juno, and her satellite were able to return home to her family. Finally Juno and her satellite were able to return home to her family. Finally Juno and her satellite, were able to return home to her family. Finally, Juno and her satellite were able to return home to her family.

Answers

Answer:

Finally, Juno and her satellite were able to return home to her family.

Step-by-step explanation:

Answer:

Finally, Juno and her satellite were able to return home to her family

Step-by-step explanation:

Simplify the expression
3+4·10 – 8

Answers

Answer:

35

Step-by-step explanation:

one word: PEMDAS. technically they are all a bunch of words but whatever...

P: parentheses

e: exponents

m: multiply

d: divide

a: add

s: subtract

first we multiply 4*10 since that's first on the list

4*10=40

we have

3+40-8

then we add

3+40

which is 43

then we subtract 8 from it as we have 43-8

which is in the end:

35

35

Step by step equation
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