An exponential function is given by the equation y=3x. Using the points xx and x+1x+1, show that the y-values increase by a factor of 3 between any two points separated by x2−x1=1.(4 points)

Answers

Answer 1

Answer:

Here we have the function:

y = f(x) = 3^x

Using the values:

x and (x + 1)

We need to find that the y-value increases by a factor of 3.

So we need to prove that:

f(x + 1) = 3*f(x).

Or we can see the quotient:

f(x + 1)/f(x) = 3

Here we can find the values:

f(x + 1) = y = 3^(x + 1)

f(x) = y' = 3^x

If we take the quotient, we get:

[tex]\frac{f(x + 1)}{f(x)} = \frac{3^{x + 1}}{3^x}[/tex]

Here we can use the properties:

[tex]a^n*a^m = a^{n + m}[/tex]

[tex]\frac{a^n}{a^m} = a^{n - m}[/tex]

Using these in the quotient equation we get:

[tex]\frac{f(x + 1)}{f(x)} = \frac{3^{x + 1}}{3^x} = \frac{3^x*3^1}{3^x} = \frac{3^x}{3^x}*3 = 1*3 = 3[/tex]

Then:

[tex]\frac{f(x + 1)}{f(x)} = 3[/tex]

[tex]f(x + 1) = 3*f(x)[/tex]

So we found that the y-value increases by a factor of 3 between any two points x₂ and x₁ such that: x₂ - x₁ = 1.


Related Questions

Which function has the greater maximum value: f(x) = -2x2 + 8x-1, or g(x),
the function in the graph?

A. Ax)
B. g(x)
C. The functions have the same maximum value.

Answers

Answer:

It’s f(x)

Step-by-step explanation:

.In a survey, 7/20 of the students in fifth
grade said their family buys organic
vegetables. What decimal represents
the portion of students whose families
buy organic vegetables?

Answers

Answer:

Road shimmer

Wiggling the vision

Heat heat waves

I'm swimming in a mirror

Road shimmer

Wiggling the vision

Heat heat waves

I'm swimming in a

Sometimes, all I think about is you

Late nights in the middle of June

Heat waves been faking me out

Can't make you happier now

Sometimes, all I think about is you

Late nights in the middle of June

Heat waves been faking me out

Can't make you happier now

Usually I put

Something on TV

So we never think

About you and me

But today I see

Our reflections

Clearly in Hollywood

Laying on the screen

You just need a better life than this

You need something I can never give

Fake water all across the road

It's gone now the night has come but

Sometimes, all I think about is you

Late nights in the middle of June

Heat waves been faking me out…

Please help u have till 3:10 pm cst time - Texas

Answers

Answer:

1/8 is equal to 0.125

5/8 is equivalent to the other fraction 10/16 and in decimal form it is 0.625

• Check your work when you're done.
Your Assignment
A bag contains 5 marbles. There are 3 yellow marbles and 2 red marbles.
Suppose that Glen chooses a marble first and then Kris chooses one.
Answer the questions to show the probability that Kris will get a yellow marble if
Glen chooses a yellow one first.
1. What is the probability that Glen will get a yellow marble? Show how you
calculated this probability.
Write your answer in the space below.
i

Answers

If Glen get a yellow marble first then we have 2 yellow marbles...probability that Glen will get yellow marble is 2/5(we have just 2 yellow now and the total is 5)
2/5-answer☺️

Given f(x) = -x + 1, solve for x when f(x) = 0.

Answers

Answer:

f(x) = -x + 1

0 = -x + 1

x = 1

Step-by-step explanation:

You put 0 in place of f(x).

50 PTS!!!!
PLEASE LOOK AT THE SCREENSHOT AND ANSWER:
Which kind of model best describes this set of data?

Answers

Answer:

that is the correct answer

Its quadratric data

Find the missing angle.
Round to the nearest tenth.
B = 50°
b = 8
a = 10
A=

Answers

Answer: 73.2 degrees

Step-by-step explanation:

Have a great summer

One bow requires 3.2 inches of ribbon. How many
bows can be made from 304 inches of ribbon?

Answers

Answer:

95

Step-by-step explanation:

304/3.2 = 95

Answer:

4

Step-by-step explanation:First, we convert feet into inches. A foot equals 12 inches so 3 feet equal 36 inches. Then, we divide by 8. 36/8 = 4.5, and we can say that 4 bows can be made.

Please tell me the answer and help me explain how it’s the right answer

Answers

Answer: number greater than -8 includes -2, 1/4, 2.6, 4

Explanation:


Answer:

Answers = a , c, d, e

Step-by-step explanation:

Absolute value of -8 = 8

Find the absolute values of the other numbers

The other numbers have to be less than 8 or else they are less than -8

Absolute value of 2.6 = 2.6 .   2.6<8

Absolute value of -10 = 10 .     10 >8 .      not correct

Absolute value of -2 = 2 .         2<8

Absolute value of 4 = 4 .           4<8

Absolute value of 1/4 = 1/4 .       1/4<8

Absolute value of -8.5 = 8.5 .     8.5>8 .   not correct

About Absolute Value:

Absolute value is the distance from 0 on the number line.

The number 5 is 5 units from 0

The number -5 is also 5 units from the 0, except from the opposite side

Absolute value states that negative numbers have a positive absolute value and a positive number has a positive absolute value.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

what is [tex]\frac{69}{100}[/tex] in simplest form?

Answers

Answer:

It’s already in simplest form but in decimal form it is 0.69
That would be it’s simplest form

Giving brainlist to whoever answers

Answers

I think z because if you flip the shape around it will create the same shape as z
it is z ! i hope you get it right!

Determine the center and radius of the following circle equation:
+ y2 – 123 + 8y – 48 = 0

Answers

It’s 10


Do you want the steps on how to get it?

Answer:

it's 10

Step-by-step explanation:

don't know the steps

I am very confused- Can someone help within an hour-

Answers

Answer: 195 CM

Step-by-step explanation:

Volume: Length x Width x Height

“First we have to break it into 2 shapes”

“Let’s solve the top shape!!”

The length is 5 the width is 3 and the height is 4.

Volume = 5 x 3 x 4 = 60

Now the bottom shape

The length is 9 the Width is 5 and the Height is 3

The height isn’t given so we must do some math

Subtract the 7 from 4 = 7 - 4 = 3

Volume = 9 x 5 x 3 = 135

Finally, 135 + 60 = 195 cm

What value of a would make the graph of f(x) = ax² open up?

Answers

Answer:

dont knohfxvggxhb cbbvc

62X + 310 =
2542 Find X

Answers

Answer:

36

Step-by-step explanation:

62x + 310 = 2542

62x = 2232

x = 36

Answer:

36

Step-by-step explanation:

62x + 310 = 2542

Subtract 310 from both sides

62x = 2,232

Then Divide by 62

x = 36

Enjoy.

Here is the histogram of a data distribution.

What is the shape of this distribution?
A. Bimodal symmetric
B. Uniform
c. Unimodal symmetric
D. Bimodal skewed
E. Unimodal skewed

Answers

Answer:

Uniform

Step-by-step explanation:

We don't have any peaks in the histogram, so its neither unimodal or bimodal leaving only uniform as the answer.

The shape of this distribution, histogram is Unimodal skewed type. The correct option is E.

What is histogram?

A histogram represents the graphical representation of the distribution of data. The histogram is indicated by using a set of rectangles adjacent to each other where each bar represent a kind of data. The histogram doesn't involve any gaps between the two successive bars.

The histogram would be classified into different types based on the frequency distribution of the data.

Based on the direction of the tail, the skewed distribution may be either right-skewed or left skewed.

Since skewed distribution is asymmetrical as a limit which is natural resists end results on one side.

Threfore, the correct option is E.

To know more about histogram, visit;

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please and thank you , 10 points​

Answers

i don’t know the answer but pls do not click the link the other person sent!! it is a scam

What is an equation of a line that has the points (2, 4) and (-3, 5)?

Answers

Answer:

y= -1/5x+4.4

Step-by-step explanation:

this is written in slop-intercept form

Answer:

y=-1/5x+4.4

Step-by-step explanation:

The answer is the answer above

Which of the following pairs of events are disjoint (mutually exclusive)?
a) A: odd numbers; B: the number 5

b) A: even numbers; B: numbers greater than 10
c)A: numbers less than 5; B: all negative numbers
d)A: numbers above 100; B: numbers less than -200​

Answers

Answer:

d

Step-by-step explanation:

d because there are no numbers common to  both sets

Disjoint sets are those sets that have no common values between the sets.

A: numbers above 100; B: numbers less than -200​ is a disjoint set.

Option D is the correct answer.

What is a set?

A set is a collection of items where there are operations such as:

Union of sets, the intersection of sets, complements of sets.

We have,

Disjoint sets are those sets that have no common values between the sets.

a) A: odd numbers; B: the number 5

Set A = {1, 3, 5, 7, 9,.....}

Set B = {5}

A ∩ B = {5}

This is not a disjoint set.

b) A: even numbers; B: numbers greater than 10

A =  {2, 4, 6, 8, 10, , , }

B = {11, 12, 13, 14, 15, 16, 18,,,,,}

A ∩ B = {12, 14, 16, 18,,,}

This is not a disjoint set.

c) A: numbers less than 5; B: all negative numbers

A = {, , ,, -3, -2, -1, 0, 1, 2, 3, 4}

B = {, , , , -3, -2, -1}

A ∩ B = { , , , , -3, -2, -1}

This is not a disjoint set.

d) A: numbers above 100; B: numbers less than -200​

A = {101, 102, 103, 104, ,,,,,,}

B = {, , , , -204, -203, -202, -201}

A ∩ B = Ф

There are no common values between set A and set B.

This is a disjoint set.

Thus,

A: numbers above 100; B: numbers less than -200​ is a disjoint set.

Option D is the correct answer.

Learn more about sets here:

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8 x 9 = 8 x(5+ _)
= (8 x 5) + (8 x _)
= 40 + _
= _

Answers

Answer:

B

Step-by-step explanation:

i hate math

Please help! I will give Brainliest!
Who is correct?

Answers

Answer:

Dylan Is Correct

Step-by-step explanation:

Answer:

Dylan is correct

Step-by-step explanation:

HELPP
Simplify: (x^3y^-3/ x^2y) ^-3

Answers

Answer:

A i the answer

Step-by-step explanation:


can someone help? i’ll give brainliest!!

Answers

Answer:

Add the numbers that have the same variables and exponents. Hope this helps!

Step-by-step explanation:

Answer:

-3x³ - 4x - 9

Step-by-step explanation:

-5x + x - 6x³ - 4 - 5  + 6x³ - 3x³

-6x³ + 6x³ - 3x³ - 5x + x - 4 - 5

-3x³ - 4x - 9

if tanθcscθ = 3, find the value of cosθ

Answers

Answer:

1.5

Step-by-step explanation:

[tex]\huge{ \mathfrak{  \underline{ Answer }\:  \:  ✓ }}[/tex]

Let's Solve :

[tex] \tan( \theta) \csc(\theta) = 3[/tex]

[tex] \dfrac{ \sin(\theta) }{ \cos(\theta) } \times \dfrac{1}{ \sin(\theta) } = 3[/tex]

[tex] \dfrac{1}{ \cos( \theta) } = 3[/tex]

[tex] \cos(\theta) = \dfrac{1}{3} [/tex]

_____________________________

[tex]\mathrm{ \#TeeNForeveR}[/tex]

A school has 840 pupils and 40 teachers.
Find the ratio of the number of pupils to the number of teachers.
Give your ratio in the form n : 1.

Answers

Answer:

21:1

Step-by-step explanation:

840/40 = 21

Every teacher has 21 atusents

For every 21 stutent theare is  1 teacher

40 teachers .Every teacher 21 students  40 x 21 = 840

The mean absolute deviation is 46,54,43,57,50,62,78,42

Answers

8.75 hope this helps

The mean absolute deviation (MAD) of the given set of numbers is 8.75.

What is the mean absolute deviation (MAD)?

The mean absolute deviation (MAD) of a group of data points is a statistical metric used to evaluate its dispersion or variability. It indicates how far off the data values are from the mean (average) of the data collection.

Let's calculate the MAD for the given set of numbers: 46, 54, 43, 57, 50, 62, 78, 42.

Calculate the mean:

Mean = (46 + 54 + 43 + 57 + 50 + 62 + 78 + 42) / 8 = 432 / 8 = 54

Find the absolute difference between each number and the mean:

|46 - 54| = 8

|54 - 54| = 0

|43 - 54| = 11

|57 - 54| = 3

|50 - 54| = 4

|62 - 54| = 8

|78 - 54| = 24

|42 - 54| = 12

Calculate the average of these absolute differences:

MAD = (8 + 0 + 11 + 3 + 4 + 8 + 24 + 12) / 8 = 70 / 8 = 8.75

Therefore, the mean absolute deviation (MAD) of the given set of numbers is 8.75.

Learn more about mean absolute deviation here:

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3)
1
Find the slope of a line parallel to y = 2x +3.
A)
-2
B)
1
2
C)
1
2
2

Answers

Answer:

1/2

Step-by-step explanation:

Parallel lines always have the same slope

at a fall festival student council sold two types of drinks hot chocolate in apple cider how many cups of apples are sold​

Answers

Answer:

add a picture so i can see and help

Step-by-step explanation:

Answer:

your questions is completing

Find the volume and surface area of the composite figure shown below if the figure is built with unit cubes.

Answers

Answer:

the volume is 18 and the surface area is 46

Step-by-step explanation:

The volume of the cube will be and the surface area of the cube will be square units.

What is volume?

Volume is defined as the space covered by any solid body in the three-dimensional plane. The volume of the cube will be calculated by multiplying all three sides of the cube.

The volume will be calculated as below:-

The formula to calculate the volume = l x w x h

The volume of the first part = 2 x 2 x 3 = 12 cubic units

The volume of the Second part = 2 x 2 x 1 = 4 cubic units

The volume of the third part  = 2 x 1 x 1 = 2

Total volume of the cube  = 12 + 4 + 2 = 18 cubic units.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

The surface area will be calculated as below:-

Surface area of the base = 2 ( 4 x 2) + 2( 2x 1) + 2 ( 4x 1) = 28

Surface area of the middle = 2 ( 3 x 2 ) + 2 ( 2 x 1 ) + 2 ( 3 x 1) = 22

Surface area of the upper side = 2 ( 2 x 2) +2 ( 1 x 2 ) + 2 ( 1 x 2) = 16

The total surface area is calculated as below:-

Total = 28 + 22 + 16 = 66 square units.

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Ria is 6 years older than her brother. Fourteen years ago, she was twice as old as he was. How old is each now?

Answers

answer:
ria is 18 and the brother is 12.

Answer

ria is 26 and her brother is 20

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