Given the function f(x)=4(2)2, Section A is from x=1 to x=2 and section B is from x=3 to x=4. Part A: find the average rate of change of each section. 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.

Answers

Answer 1

Answer:

I found thois from someone else asking this queetion so gope it helps.

Step-by-step explanation:

I'm sure you want your functions to appear as perfectly formed as possible so that others can help you.  f(x) = 4(2)x should be written with the " ^ " sign to denote exponentation:  f(x) = 4(2)^x

                                                                                     f(b) - f(a)

The formula for "average rate of change" is a.r.c. = --------------

                                                                                          b - a

                                   change in function value

This is equivalent to  ---------------------------------------

                                           change in x value

For Section A:  x changes from 1 to 2 and the function changes from 4(2)^1 to  4(2)^2:  8 to 16.  Thus, "change in function value" is 8 for a 1-unit change in x from 1 to 2.  Thus, in this Section, the a.r.c. is:

                8

              ------ = 8 units    (Section A)

                 1

Section B:  x changes from 3 to 4, a net change of 1 unit:  f(x) changes from

4(2)^3 to 4(2)^4, or 32 to 256, a net change of 224 units.  Thus, the a.r.c. is

       224 units

     ----------------- = 224 units (Section B)

           1 unit

The a.r.c for Section B is 28 times greater than the a.r.c. for Section A.

This change in outcome is so great because the function f(x) is an exponential function; as x increases in unit steps, the function increases much faster (we say "exponentially").


Related Questions

Help please here is a picture:

Answers

Answer:

2 1/3, 2 1/4, 2 3/7

Step-by-step explanation:

Mixed Fractions

Mixed fractions are made of an integer part followed by a proper fraction.

Some examples of mixed fractions are:

3 1/2, -4 5/8, 2 2/3

Between two consecutive integers a and a+1, there are infinitely many fractions. The centered number is a 1/2. Any number with its improper fraction part less than 1/2 is closer to a than to a+1.

In our problem, Jayne bought between 2 and 3 pounds of granola. We need to provide a mixed number that is closer to 2 pounds than to 3 pounds.

We can select any number with integer part 2 and a proper fraction less than 1/2.

Examples could be :

2 1/3, 2 1/4, 2 3/7

All of them are less than 2.5

using the arithmetic sequence 7 10 13 16 find the 6th term of the sequence ​

Answers

22 is the correct answer

HELP!!!!! will give brainliest to the right answer ​

Answers

Answer:

domain is x is an element of all real numbers, or {xer}, and the range is {3.5}

Step-by-step explanation:

since x stretches the whole way it is all real numbers, and y only touches one point on the graph so it has to be a single point

Which equations are equivalent? Select all that apply.

2n + 4n + 3 = 51
3n + 4 + 5n = 52
3(2n + 6) = 36
8n + 4 = 52
4(2n + 1) = 52

Answers

3n+4+5n=52, 8n+4=52, and 4(2n+1)=52

A storage company designs a rectangular box with an open top that has a volume of 220 in3. Each box has a length that is three times its width. Calculate the minimum surface area of one of these boxes. Round your answer to three decimal places.

Answers

Answer:

191.016 in²

Step-by-step explanation:

Let the volume of the cube be V = lwh where l = length of box, w = width of box and h = height of box.

Now l = 3w.

So, V = lwh = (3w)wh = 3w²h

h = V/3w²

Since the rectangular box is open at the top, its total surface area is A = lw + 2lh + 2wh

substituting l = 3w, we have

= (3w)w + 2h(l + w)

= 3w + 2h(3w + w)

= 3w² + 2h(4w)

= 3w² + 8wh

substituting h = V/3w²

= 3w² + 8w(V/3w²)

A = 3w² + 8V/3w

Differentiating A with respect to w and equating it to zero, we have

dA/dw = d[3w² + 8V/3w]dw

dA/dw = d3w²/dw + d(8V/3w)/dw

dA/dw = 6w - 8V/3w²

dA/dw = 0

6w - 8V/3w² = 0

6w = 8V/3w²

6w³ = 8V/3

w³ = 8V/(3 × 6)

w³ = 4V/9

w = ∛(4V/9)

substituting V = 220 in³, we find the minimum value for the width

w = ∛(4 × 220 in³/9)

w = ∛97.7778

w = 4.607 in

To determine if this is a minimum value of width which gives minimum area, we take the second derivative of A. So,

d²A/dw² = d(6w - 8V/3w²)/dw

= 6 + 16V/3w³

substituting w³ = 4V/9, we have

d²A/dw² = 6 + 16V/3(4V/9)

= 6 + (16 × 9)/(3 × 4)

= 6 + 4 × 3

= 6 + 12

= 18

Since d²A/dw² = 18 > 0 , w = ∛(4V/9) = 4.607 in gives a minimum for the surface area.

So, we calculate this area by substituting w = 4.608 in. So,

A = 3w² + 8V/3w

= 3 × (4.607 in)² + (8 × 220 in³)/(3 × 4.607 in)

= 63.6733 in² + 1,760 in³/13.821 in

= 63.6733 in² + 127.3424 in²

= 191.0157 in²

≅ 191.016 in² to three decimal places.

Chang spent a total of $80 at the grocery store. Of this amount, he spent $36 on fruit. What percentage of the total did he spend on fruit?

Answers

Answer: 28 percent i believe

Step-by-step explanation:

Answer:

brandoncardona2007

Step-by-step explanation:

They are always right no matter what

Which statement is false? All points with an x-value of 3 are located in Quadrant I. There is only one point on the coordinate plane that is on both the x- and y-axes. All points with an x-value of 0 are located on the y-axis. There is only one point on the coordinate plane with an x-value of 2 and a y-value of 2.

Answers

Answer: Choice A)  All points with an x-value of 3 are located in Quadrant I.

We can show it is false through the use of a counter example. For instance, the point (3, -5) is not in quadrant 1, but rather in quadrant 4.

We would need to say "all points with x value 3 and positive y value" to ensure the point is in quadrant 1.

The false statement:

All points with an x-value of 3 are located in Quadrant I.

What are coordinates?

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

From the given choices:

Let the statement is true.

All points with an x-value of 3 are located in Quadrant I.

Let the coordinate point (3, -7)

This point lies in the fourth quadrant.

Which is contradiction.

Therefore, the statement is false.

To learn more about the coordinates;

https://brainly.com/question/27749090

#SPJ6

what is 9k + 1 = ─9 + 7k solved for the variable???

Answers

Answer:

k = -5

Step-by-step explanation:

The variable is k

9k + 1 = -9 + 7k

-7k        -1

2k = -10

2k/2  -10/2

k = -5

:)

In how many ways can a president, vice president, and secretary be chosen from a class of 20 girls and 30 boys if the president must be a girl and the vice president a boy?

Answers

Given:

Number of girls = 20

Number of boys = 30

The president must be a girl and the vice president a boy

To find:

Number of ways to choose a president, vice president, and secretary.

Solution:

The president must be a girl and the vice president a boy. So, out of three students 1 is girl and 1 is boy. Third student can be a girl or a boy.

Total number of ways = Selecting 2 boys and 1 girl +  Selecting 1 boy and 2 girls

[tex]=^{30}C_2\times ^{20}C_1+^{30}C_1\times ^{20}C_2[/tex]

[tex]=\dfrac{30!}{2!(30-2)!}\times \dfrac{20!}{1!(20-1)!}+\dfrac{30!}{1!(30-1)!}\times \dfrac{20!}{2!(20-2)!}[/tex]

[tex]=\dfrac{30\times 29\times 28!}{2\times 1\times 28!}\times \dfrac{20\times 19!}{19!}+\dfrac{30\times 29!}{29!}\times \dfrac{20\times 19\times 18!}{2\times 1\times 18!}[/tex]

[tex]=\dfrac{30\times 29}{2}\times 20+20\times \dfrac{20\times 19}{2}[/tex]

[tex]=8700+3800[/tex]

[tex]=12500[/tex]

Therefore, the required number of ways is 12500.

daca stim cel mai mare divizor comun si cel mai mic multiplu comun,in ce mod aflam produsul? (raspunsuri troll iau raport) (troll answers will get reported)

Answers

Answer: i think this is romanian? so here is the answer in romanian

Pur și simplu, cel mai mare factor comun al lui a și b atunci când este înmulțit cu cel mai mic comun al lui a și b este egal cu produsul lui a și b ....

Puteți determina LCM de 12 și 16 folosind două metode

Step-by-step explanation:

Largest prime factor of 35 x the smallest prime factor of 15

Answers

Answer:

7x3=21 ... i think

Step-by-step explanation:

the factor of 35 is 1,5,7 and 35 but 7 is the largest prime number like the factors of 15 is 1,3,5 and 15 but 3 is the smallest prime number according to the question the answer is 7x3+21

You have a budget of $1,900 per week for employees. Employees are pald $11 per hour and work 40 hours per week.
Ignoring overhead, how many employees can you hire ?

Answers

 [tex]\boldsymbol{4}[/tex] employees were hired by the company.

Define unit method.

Amount of total budget [tex]=\$1,900[/tex]

Amount paid to an employee per hour [tex]=\$11[/tex]

Number of hours for which an employee worked per week [tex]=40[/tex]

So,

Total amount paid to an employee [tex]=11\times 40[/tex]

                                                          [tex]=\$440[/tex]

Number of employees hired [tex]=4.3[/tex]

                                               [tex]\approx 4[/tex]

So, [tex]\boldsymbol{4}[/tex] employees were hired by the company.

Find out more information about unit method here:

https://brainly.com/question/15052343?referrer=searchResults

Ignoring overhead, you can hire 4 employees.

What is division?

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

You have a budget of $1,900 per week for employees.

Employees are paid $11 per hour and work 40 hours per week.

That means,

11 x 40 = $440 per week.

The number of employees = 1900/440

= 4.3

≈ 4

Therefore, 4 number of employees.

To learn more about the division;

https://brainly.com/question/13263114

#SPJ2

Identify the method that will be used in solving for X
5+x=3/4
A• distributive property
B• multiplication property of equality
C• division property of equality
D• subtraction property of equality

Answers

Answer:D• subtraction property of equality

Step-by-step explanation:subtract 3/4  on both sides?????

D. Subtraction property of equality

The sum of two numbers is fifteen. One number is five more than the other. Find the numbers.

Note: List numbers with a comma separating them, e.g. 5,12.

Answers

Answer:

5,10

Step-by-step explanation:

10 is 5 more than 5 therefore

5+10=15

Answer:

5,2,2,2,2,2

Step-by-step explanation:

2+2+2+2+2=10

10+5=15

How do you do this please explain!

Answers

Since 4 pastries is $10. Divide 10 by 4 to find out how much it cost per pastry.
10/4 = $2.5 per pastry

$2.5 * 9 pastries = cost
For 9 pastries, it cost $22.50

Plug it into the table :)

Get it right and ill paypal 25$ if ur fast

Answers

ight what do i gotta answer tho

CAN SOMEBODY PLEASE HELO ME!?!?!?

The radius of the unit circle is equal to_____.
•2π
•1
•2
•π​

Answers

Answer:

r =1

Step-by-step explanation:

The radius of unit circle is 1

Answer:

1

Step-by-step explanation:

simply 8×4³+2×4⁴ giving you answer in the form of 4^b​

Answers

Answer:

4^5

Step-by-step explanation:

8×4³+2×4⁴

4×2×4^3+2×4^4

4^4×2+2×4^4

4^4(2+2)

4^4×4

4^5

So answer is 4^5

What value of y makes the equation below true?
2y – 25 = 19
44
A
B
22
C
с
-3
oo
D
-6


Please hurry

Answers

Answer:

b

Step-by-step explanation:

2*22 = 44

44-25 = 19

A sweater originally priced at 80 dollars was marked down 25% what was the sale price of the sweater

Answers

Answer:

$60

Step-by-step explanation:

just is

You plan to run 2 miles, but you only make it \frac{3}{4}
​4

​3
​​ of the way. How many miles did you run in total?

Answers

Answer:

1.5 miles

Step-by-step explanation:

Wayne raked 30 bags of leaves in 3 hours. If he raked the same number of bags each hour, how many bags of leaves did he rake in 1 hour?

Answers

Answer:

he raked 10 bags each hour

30/3 = 10

10 bags each hour
He rakED

What percent of 78 is 16?

Answers

Answer:

78/16=

39/8=

19.5/4= 4.80805

16 is 20.51% of the number 78.

What is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let x percent of 78 is 16.

So, x% of 78 = 16

x/100 (78)= 16

78x = 1600

x= 1600/78

x = 20.51%

Hence, 20.51 percent of 78 is 16.

Learn more about Algebra here:

https://brainly.com/question/24875240

#SPJ6

I NEED HELP ... please help me.

Answers

∆STU= ∆EDC∆WVU=∆WNM

Step-by-step explanation:

here = means the similar triangle plz don't confuse. And 1. is proved by SSS axiom or SAS axiom and 2. is proved through SAS axiom will be much more better.

Answer:

1. ∆STU- 75

2. ∆WVU-55

3. 65+ 50 =115 -180= 65

help pls- 10 points- algebra 1


solve for x

-8x+14 ≥ 60 OR − 4x+50 -2

D.) There are no solutions

Answers

Answer:

-8x+14 ≥ 60

Inequality Form:

x< -23/4

Interval Notation:

(−∞,−23/4)

is y=-2x proportional

Answers

Answer:

no

Step-by-step explanation:

Answer:

Yes, if you are referring to proportionality in general. No if you are referring to a direct proportionality.

Step-by-step explanation:

y = -2x is negatively proportional so it is not directly proportional because y or one quantity decreases when x or another quantity increases. In a directly proportional relationship, as one quantity increases another quantity must increase at the same rate, in other words both must increase thus be positive. When something is proportional it has a constant ratio, and relation.

Direct proportionality or variation is represented by y ∝ x, where ∝ is the symbol used to represent proportionality.

y = kx where k is the constant of proportionality.

Where k = y/x.


What is the equation for
7x - 4/y =10
in the form y = mx + b?

Answers

Answer:

Step-by-step explanation:

assume the equation is (7x-4)/y=10

10y= 7x-4 didvide both sides by 10

y= (7/10)*x - (2/5)

m=7/10

b=-2/5

The equation for 7x - 4/y =10 in the form y = mx + b . The equation in the form

[tex]\(y = mx + b\) is: \[y = \frac{4}{7x - 10}\][/tex]

To rewrite the equation in the form  we need to  [tex]\(y = mx + b\),[/tex]  isolate the term involving y on one side of the equation. Here's the step-by-step process:

Step 1: Add  [tex]\(\frac{4}{y}\)[/tex]  to both sides of the equation to isolate the 7x term on the left side:

[tex]\[7x = 10 + \frac{4}{y}\][/tex]

Step 2: Get rid of the fraction by multiplying both sides of the equation by y:

[tex]\[7xy = 10y + 4\][/tex]

Step 3: Now, we want to express  y alone on one side. To do this, subtract 10y  from both sides:

[tex]\[7xy = 10y + 4\][/tex]

Step 4: Factor out y on the left side:

[tex]\[y(7x - 10) = 4\][/tex]

Step 5: Finally, divide both sides by to solve for  [tex]\((7x - 10)\)[/tex]

[tex]\[y = \frac{4}{7x - 10}\][/tex]

Now, the equation is in the form where [tex]\(y = mx + b\), \(m\)[/tex] is the coefficient of x and b is the constant term. In this case,[tex]\(m = \frac{4}{7x - 10}\) and \(b\)[/tex]  is equal to 0.

To know more about equation:

https://brainly.com/question/2419445

#SPJ2

u guys are very helpful <3​

Answers

35 degrees is the answer for x

Answer:

x=35

Step-by-step explanation:

70+75is 145

and a triangle is equal to 180 degrees

so 180-145 gives you 35 :)

Is 518 decimal number

Answers

Answer:

no

Step-by-step explanation:

because there is supposed to be a decimal point for example 5.18 there needs to be a period

Answer:

what do you mean there is not decimal in the number you could make it a decimal tho

it would be 5.18 as a decimal

Step-by-step explanation:

Two angles of a triangle have the same measure and the third one is 30 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle.

Answers

Answer:

75 degrees

Step-by-step explanation:

Isosceles triangle with 3rd angle being 30 degrees:

2x + 30 = 180

2x = 150

X = 75

Ответ равен = 75 ниже фото
Other Questions
Hey, I dont understand the graphing part of inequalities. In the metric system, which prefix would you use for "1/100"?A. Milli-B. HectoC. Kilo-D. Centi- Consider the line that passes through each pair of given points, and decide what type of slope the line has.(2, 4) and (5, 1)undefined slope(3,5) and (-1,2)negative slope(-7, 8) and (-7,0)positive slope(6.-3) and (4, -3)zero slope can someone do 1,3,4,8 and 9 pls Please help me please thank you so much in advance A manufacturer of scented candles is preparing to produce five new candles with fragrances of peppermint, cinnamon, lemon, spice pumpkin, and pine scents to sell for the holiday season. To track the sale of the new scented candles you will need to create a program that should use two parallel element arrays. An array that will hold the names of the 5 new scented candles and another array that holds the count of the 5 new scented candles that are sold over the next couple of months. The program will track the fragrance type of the candle purchased and the number of candles sold for each fragrance. The program should also generate a report that displays the fragrance type of the 1.largest number and 2.smallest number of candles sold and the 3.total sales of all candles purchased. PEOPLE HELP. ASAPMy foster brother is leaving soon and I am really sad. He has been with us for a year and a half now and he is going to live with his grandma. :( She smokes and I am afraid he might get abused. How would you cope with this is he felt like your brother??!! Pls help me ASAP.(will give brainliest to best answer) :((((((( chloroplast (has chlorophyll inside) is where sunlight breaks apart water and carbon dioxide to form sugar and oxygen true or false Solve for a in terms of b, c, and d: ab+c=dSolve for x in terms of p and q: 3x + p = 9please show workthanks Please help! I will give brainliest! (6^96^5)/ 6^15 How can the use of pundits or "talking heads" increase the trustworthiness of news media? Their expertise could strengthen the evidence supporting the media's claims. Their authority as experienced journalists could increase the media's believability. Their connections to multiple media sources help the media gain popularity. Their skill at creating fake news can help the press manipulate viewers. Lee el siguiente poema.Juventud, divino tesoro.Juventud, divino tesoro, ya te vas para no volver! Cuando quiero llorar, no lloro y a veces lloro sin quererPlural ha sido la celeste historia de mi corazn. Era una dulce nia, en este mundo de duelo y de afliccin.Miraba como el alba pura; sonrea como una flor. Era su cabellera obscura hecha de noche y de dolor.Yo era tmido como un nio. Ella, naturalmente, fue, para mi amor hecho de armio, Herodas y SalomJuventud, divino tesoro, ya te vas para no volver! Cuando quiero llorar, no lloro y a veces lloro sin quererY ms consoladora y ms halagadora y expresiva, la otra fue ms sensitiva cual no pens encontrar jams.Pues a su continua ternura una pasin violenta una. En un peplo de gasa pura una bacante se envolvaEn sus brazos tom mi ensueo y lo arrull como a un beb Y te mat, triste y pequeo, falto de luz, falto de feJuventud, divino tesoro, te fuiste para no volver! Cuando quiero llorar, no lloroy a veces lloro sin quererOtra juzg que era mi boca el estuche de su pasin; y que me roera, loca, con sus dientes el corazn.Poniendo en un amor de exceso la mira de su voluntad, mientras eran abrazo y beso sntesis de la eternidad;y de nuestra carne ligera imaginar siempre un Edn, sin pensar que la Primavera y la carne acaban tambinResponde en tu cuaderno-En este poema encontramos la mayora de los temas modernistas, bscalos y explcalos brevemente. To paint a house, a painting company charges a flat rate of $500 for supplies, plus $50 for each hour of labor.Find the slope of the line, What is the meaning of the slope in this context? Read the excerpt from Weve Got a Job by Cynthia Levinson.At that point, things got even scarier for the marchers. Connor rolled up in a massive white car shaped and outfitted like a tank, complete with gun turrets. "Connor told them to arrest [us], James said. "We were crammed into the paddy wagons that were meant to hold maybe eight people at the mosttwo in [each of] the four cubicles that they had. They crammed three and four of us into one cubicle and they continued to press the door until they got it shut and locked and [had] us taken off to jail.As soon as Jamess group was hauled away, Bevel released the next group of fifty students. When that batch was arrested, the next group burst from the church.Which pair of adjectives best describes the shared experience of the student groups?A - peaceful, carefreeB - angry, aggressiveC - scared, determinedD - cautious, resistant Decide which indirect object pronoun should replace the underlined word.Parle Paul.luileur Difference between Democrat, Republican, Green, and Libertarian Users can customize their Windows device by going to the Control Panel under __________. What is the change in momentum of a 4 kg object accelerating from 10 m/s to 12 m/s? In this problem what is the change in velocity when was the last Census of Nepal taken Which best completes the sentence and avoidswordiness? HELP PLZ IM GETTING TIMED.. I think I have a answer but Im not 100% totally hungrycompletely starvedfamishedvery hungry