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

can i get the answer and the explination on how to do this plz? thank uuu =) NO LINKS PLZ

Answers

Answer:

The answer is 94.5

Step-by-step:

This is actually quite simple. Although, in order to do this you will need a calculator. First, you identify which trigonomic function you will use in order to find the value of x. for this problem you need to use the COS function. The equation for this is COS67= 67/x. Because you are trying to find x you would multiply each side by x. now the equation is xCOS67= 67. because you still can't find the value of x by doing this you will need to get x by itself. To get x by itself divide each side by COS67. the equation is now x= 94/ COS67. This is where the calculator comes in. On the calculator enter 94 divided by 67 then COS function. This gives you the measure of RS.

A recent taste test showed that 85% of people liked a new chicken sandwich recently added to a restaurant’s menu. The restaurant manager claimed that only 68% liked the new sandwich. To determine whether this sample supports the population proportion of 0.85, a simulation of 100 trials is run, each with a sample size of 30 and a point estimate of 0.85. The minimum sample proportion from the simulation was 0.66 and the maximum sample proportion from the simulation was 0.88.


a) Estimate the margin of error using the half the range method.


b) Use your margin of error to find the interval estimate.


c) Based on the computed interval estimate, is the restaurant manager’s claim that 68% of people liked the new sandwich valid? Explain your answer.

Answers

Answer:

a) The margin of error = 0.11

b) The interval estimate = (0.74, 0.96)

c) Not valid because 68% = 0.68 is less than the values in the interval estimate

Step-by-step explanation:

The statistical data from the population and the simulation are;

The percentage of the people that liked the new chicken sandwich = 85% = The population proportion

The percentage the restaurant manager claims liked the new sandwich = 68%

The number of trials of the simulation = 100 trials

The sample size of each trial = 30

The point estimate of each trial = 0.85

The minimum sample proportion = 0.66

The maximum sample proportion = 0.88

a) The confidence interval = (0.66, 0.88)

By the half the range method, the margin of error is given by half the width of the confidence interval

∴ The margin of error, MOE = (0.88 - 0.66)/2 = 0.11

b) The interval estimate are the expected range of numbers for a parameters

The interval estimate = The point estimate ± MOE

∴ The interval estimate = 0.85 ± 0.11 = (0.74, 0.96)

Given that the manager's claim of 68% is not within the interval estimate, the manager's claim is not valid based on the expected values for the people that liked the new sandwich found with the point estimate and the margin of error

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

thanks for the help guys

Answers

Answer:

Um.... Your welcome(confuse face), but also I see you got a bad grade. I wish I could've help you at least you would've gotten one answer right.

Step-by-step explanation:

How can I find the height of a pyramid that has a base of 13m and a 13m lateral height

Answers

Answer:

Dnnd

Step-by-step explanation:

Answer:

The lateral faces meet at a common vertex. The height of the pyramid is the perpendicular distance from the base to the vertex. A pyramid is a regular pyramid if its ... A triangular pyramid has a triangle base. regular pyramid. A right pyramid is ...

Missing

Step-by-step explanation:

I'll give BRAINLIEST PLEASE ANSWER

Answers

Answer:

C

D

Step-by-step explanation:

there's nothing to explain here. just basic

Answer: C

Step-by-step explanation: To simplify the first equation given, you use the process of elimination. There are three of the same variable, s, and that would be simplified to 3s. After that everything remains the same. Making C equivalent to the given equation.

dexter has a total of 50 red, blue and green straws if he has 20 red straws, what fraction of dexter's straws are red?

Answers

Answer:

2/5

Step-by-step explanation:

20/50 is 2/5 simplified

Answer:

20/50=2/5

Step-by-step explanation:

The volume of a cylinder is 725x cm”. The radius of the base of the cylinder is 5 cm. What is the height of the cylinder?

Answers

Determine the volume formula for the cylinder. Plug in your given volume and radius to solve for h (height). See image above
Go with the answer the other person commented their correct!

Answer this question for me

Answers

The angle size for BDC is 88

Please help me it would mean the world. Extra points!
The answer is 102m^2 provided by my teacher I just need the work.

Answers

Answer:

[tex] \displaystyle A_{ \text{triangle}} = 102 {m}^{2} [/tex]

Step-by-step explanation:

remember that,

[tex] \displaystyle A_{ \text{triangle}} = \frac{1}{2} bh[/tex]

given that,b is 17 m and h is 12m

thus substitute:

[tex] \displaystyle A_{ \text{triangle}} = \frac{1}{2} \times 17\times 12[/tex]

reduce fraction:

[tex] \displaystyle A_{ \text{triangle}} = 17\times 6[/tex]

simplify multiplication:

[tex] \displaystyle A_{ \text{triangle}} = 102 {m}^{2} [/tex]

hi
khgbv h
ljv nkmj
gv hnyhrdsrfgbnkjnbhbbbhjik

Answers

Answer:

hihi

Step-by-step explanation:

Answer:

inspiringwords love it so much

Step-by-step explanation:

The histogram shows the weights, in pounds, of checked luggage on a flight.

A graph shows weight of a bag (pounds) labeled 12 to 64 on the horizontal axis and number of bags on the vertical axis. 1 bag weighs 12 to 16 pounds. 4 bags weigh 16 to 20 pounds. 5 bags weigh 20 to 24 pounds. 6 bags weigh 24 to 28 pounds. 5 bags weigh 28 to 32 pounds. 4 bags weigh 32 to 36 pounds. 3 bags weigh 36 to 40 pounds. 1 bag weighs 40 to 44 pounds. 0 bags weigh 44 to 48 pounds. 1 bag weighs 48 to 52 pounds. 1 bag weighs 52 to 56 pounds. 1 bag weighs 56 to 60 pounds. 0 bags weigh 60 to 64 pounds.
The median weight of a checked bag is 27.5 pounds. How does the mean of the data most likely compare to the median?

The mean is most likely less than 27 pounds.
The mean is most likely exactly 27.5 pounds.
The mean is most likely about 28 pounds.
The mean is most likely more than 28 pounds.

Answers

Answer:

C, the mean is most likely about 28 lbs.

Step-by-step explanation:

The histogram shows the weights, in pounds, of checked luggage on a flight. The median weight of a checked bag is 27.5 pounds.

thats the answer because you are rounding 27.5

Hope this is helpful! :)

Have a nice day!

Answer:

c give the other person branlist

Step-by-step explanation:

In an all boys school, the heights of the student body are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What is the probability that a randomly selected student will be shorter than 63 inches tall, to the nearest thousandth?

Answers

The probability that a randomly selected student from the all-boys school will be shorter than 63 inches tall is approximately 0.9%.

To find the probability that a randomly selected student will be shorter than 63 inches tall, we need to use the standard normal distribution table or a statistical calculator.

Calculate the z-score for the value of 63 inches using the formula:

z = (X - μ) / σ

where X is the value (63 inches), μ is the mean (70 inches), and σ is the standard deviation (3 inches).

z = (63 - 70) / 3

z = -7 / 3

z = -2.3333

Now, we look up the area to the left of the z-score -2.3333 in the standard normal distribution table.

Using a standard normal distribution table, the cumulative probability for z = -2.33 (rounded to two decimal places) is approximately 0.009.

So, the probability that a randomly selected student will be shorter than 63 inches tall is approximately 0.009 or 0.9% (rounded to the nearest thousandth).

To learn more on Statistics click:

https://brainly.com/question/30218856

#SPJ4

2 x 3 x 6

(answer for points and brainliest:))

Answers

Answer:

36

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Well

lets go left to right (but it really doesn't matter as it's only multiplication the whole way)

2*3 = 6

6*6 = 36

36 is the answer

What is the median of this data set?

40, 12, 13, 33, 25, 17, 31

Answers

It will be 33, because it’s at the middle

Answer:

You separate all this number then you put them in ascending order then you start to draw a line to get your median so our median is 25

Ira walked 20 miles last week and 22 miles this week. Raj walked 1/3 the distance that Ira walked. Write an expression for the distance Raj walked

Answers

Answer:

Multiply your pace by your distance; If your pace is 9.5 minutes per mile and you ran 3 miles: 9.5 min per mi × 3 mi = 28.5 minutes = 28 minutes, 30 seconds How to calculate running speed. Divide your run distance by your run time; If you ran 2.5 miles and you ran for 20 minutes

Step-by-step explanation:

Someone plz answer this o need it done

Answers

i believe the answer is B

please give brainliest if helped :)

Explain how to factor the following:
16x^2 – 40x – 24

Answers

Answer: (x-3)(2x+1)(8)

Step-by-step explanation: First factor out the 8 to get (8)(2x^2-5x-3). So now we have what number multiply out to -6 (ab) and add up to -5. -2 and -3 work out so we manipulate the equation like (8)(2x²-2x-3x-3). Factor out 2x in the first term and -3 in the second and keep going.

Consider the following rational function fff. f(x)=\dfrac{-4x^3+7x+9}{8x^6-9x^4-2x}f(x)= 8x 6 −9x 4 −2x −4x 3 +7x+9 ​ f, left parenthesis, x, right parenthesis, equals, start fraction, minus, 4, x, cubed, plus, 7, x, plus, 9, divided by, 8, x, start superscript, 6, end superscript, minus, 9, x, start superscript, 4, end superscript, minus, 2, x, end fraction Determine fff's end behavior. f(x)\tof(x)→f, left parenthesis, x, right parenthesis, \to as x\to -\inftyx→−∞x, \to, minus, infinity. f(x)\tof(x)→f, left parenthesis, x, right parenthesis, \to as x\to \inftyx→∞x, \to, infinity.

Answers

Answer: 0 to -∞

               0 to ∞

Step-by-step explanation:

Simplify 12x6 y7 18 x3y5.

Answers

Answer:

216x^9y^12

Step-by-step explanation:

The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the font to the volume of the prism?

Answers

Answer:

A

Step-by-step explanation:

Answer:

Hey! I just took the test and the correct answer is option B.

Step-by-step explanation:

please help someone, no BOTS

Answers

Answer:

[tex]3 \times \frac{4}{9} p + 5[/tex]

3 4/9p + 5

Three and four-ninths p plus five

triangle abc is similar to triangle fgh solve for x

Answers

Answer:

A= 24

Step-by-step explanation:

First find the scale factor. so the scale factor for these two triangles is 1.5.

21 / 14 = 1.5

18 / 12 = 1.5

So you are going to multiply 16 x 1.5

That will give you 24.

HELPPPPPPPP MEEEEEEEEEEE

Answers

Answer:

12

Step-by-step explanation:

the cylindrical part of an architectural column has a height of 320 cm and a diameter of 30 cm. find the volume of the cyndrical part of the coulmn . use 3.14 for and round your answer to the nearest cubic centimeter if needed.

Answers

Hopes this helps:

Answer: 226,080 cm^3

Have a great day.

Question is in the screenshot...

Answers

Step-by-step explanation:

m L 1 = 130° (alternate interior angles)

m L 2 = 180°- m L 1 (supplementary)

= 180° - 130° = 50°

Vertical angles are supplementary

m<2

180-13050°

m<1

180-50130°

#2 find the r and h
find the surface area as we

Answers

Answer:

2) 96

3) 121

Step-by-step explanation:

2) 8 x 12 = 96

3) 11 x 11 = 121

Answer:

surface area of the cyclinder=2πr²+2πrh

=(2×3.14×12²)+(2×3.14×12×8)

=904.32+602.88

=1507.2mi²

Helpp pretty please

Answers

Answer:

b

Step-by-step explanation:

A six-sided number cube is rolled. Event A consists of rolling an even number. Event B consists of rolling a number greater than four. Match the correct sample space to each event.


1. {2, 4, 5, 6}
2. {1, 3, 5}
3. {5, 6}
4. {6}
5. {4, 5, 6}
6. {2, 4, 6)


A. Complement of A

B. Union of A and B

C. B

D. Intersection of A and B




ASAP!!!! PLEASE!!!!!​

Answers

Answer:

A-2

B-1

C-3

D-4

Step-by-step explanation:

Got it right on Edmentum

Answer:

A. 2

B. 1

C. 3

D. 4

Step-by-step explanation:

A.

A = {2, 4, 6}

Complement of A = {1, 3, 5}

Answer: 2

B.

A = {2, 4, 6}

B = {5, 6}

A U B = {2, 4, 5, 6}

Answer: 1

C.

B = {5, 6}

Answer: 3

D.

A ∩ B = {2, 4, 6} ∩ {5, 6} = {6}

Answer: 4

PLEASE HELP ME WITH THIS

Answers

Answer:

2.a..A=1/2 ×1.0×2.4=1.2m²

b.area of rectangle button=l×w=2.4×2.8=6.72m²

c.area of back =l×w=1.0×2.8=2.8m²

d.area of top =l×w=2.8×2.6=7.28m²

3.

total area =2×area of traingular side +area of rectangle button+c.area of back+area of top

=2×1.2+6.72+2.8+7.28=19.2m²

4.Assumption

total area of triangular prism is

sum of area if each faces.

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