Which exponential function is represented by the values in the table?

Which Exponential Function Is Represented By The Values In The Table?

Answers

Answer 1

Answer:

[tex]\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x[/tex]

Step-by-step explanation:

Exponential Function

The exponential function can be written with the general equation:

[tex]f(x)=A\cdot r^x[/tex]

Where A is the value when x=0 and r>0 is the ratio. If r is greater than 1, the function is increasing, if r is less than 1, the function is decreasing.

The table shows the relation between values of x and values of the function y. Note that as x increases (one by one), y decreases with a ratio of 1/2. Only the last two choices have ratios of r=1/2. We only have to test which one of them has the correct value of y=4 when x=0.

Substituting in the third function:

[tex]\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x[/tex]

[tex]\displaystyle f(0)=4\cdot\left(\frac{1}{2}\right)^0[/tex]

[tex]f(0) = 4[/tex]

This gives the correct value of f(0)=4.

Substituting in the fourth function:

[tex]\displaystyle f(x)=\frac{1}{2}\cdot\left(\frac{1}{2}\right)^x[/tex]

[tex]\displaystyle f(0)=\frac{1}{2}\cdot\left(\frac{1}{2}\right)^0[/tex]

[tex]f(0) = \frac{1}{2}[/tex]

This choice is wrong

Correct choice:

[tex]\boxed{\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x}[/tex]


Related Questions

A line passes through the point (-8, -9) and has a slope of 5/4
Write an equation in slope-intercept form for this line.

Answers

Answer:

y = 5/4x + 1

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer/how I got this answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

Answer:

y=(5/4)x(-8)+3

Step-by-step explanation:

EZ

b2-5c
b=15 & c=9
if you can show the work it would be really helpful:)

Answers

I just plugged in 15 for b and 9 for c and got -15

A store sells a pound of bananas for $0.40 and a pound of cabbage for $0.56. Can you buy more pounds of bananas or cabbage with $7? How many more pounds?

Answers

Answer:

The bananas will cost $1.38.

Step-by-step explanation:

Explanation:

Multiply the number of pounds by the price per pound.

2.51lb×$0.55lb=$1.38

15 POINTS HURRY
Write an expression that is equivalent to 5
3
r - 8
2

Answers

3 + 2 = r - 8
Add 3 + 2
5 = r - 8
Add 8 to 5 while canceling it out
13 = r
3 + 2 = 5
R =13
13 - 8 = 5
That is a true statement so an expression would be
3 + 2 = r - 8

Use synthetic division
1.
(2x3 - 5x2 + 3x + 7) = (x - 2)

Answers

Answer:

Step-by-step explanation: that should help

A group of friends wants to go to the amusement park. They have no more than $275 to spend on parking and admission. Parking is $5, and tickets cost $27 per person, including tax. Write and solve an inequality which can be used to determine r, the number of people who can go to the amusement park.

Answers

Answer:

275=27x+5

Step-by-step explanation:

10 people can go to the park

27(10)+5=275

Find the area of a rectangle whose length is 5 ½ feet long and 1 3/4 feet wide.

Answers

Answer:

11/2 x 7/4 = 77/8 = 9 5/8

Step-by-step explanation:

A light bulb is designed by revolving the graph of:

[tex]y = \frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}[/tex]

Over the interval 0 ≤ x ≤ 1/3 about the x-axis, where x and y are measured in feet. Find the surface area of the bulb and use the result to approximate the amount of glass needed to make the bulb. (Glass is 0.015 inch thick).

Answers

Answer:

[tex]\displaystyle 0.251327 \ in. \ of \ glass[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Algebra I

Terms/CoefficientsExpand by FOIL (First Outside Inside Last)Factoring

Calculus

Differentiation

Derivative Notation

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Integration

Integration Property: [tex]\displaystyle \int\limits^a_b {cf(x)} \, dx = c \int\limits^a_b {f(x)} \, dx[/tex]Fundamental Theorem of Calculus: [tex]\displaystyle \int\limits^a_b {f(x)} \, dx = F(b) - F(a)[/tex]Area between Two CurvesVolumes of RevolutionArc Length Formula: [tex]\displaystyle AL = \int\limits^a_b {\sqrt{1+ [f'(x)]^2}} \, dx[/tex]Surface Area Formula: [tex]\displaystyle SA = 2\pi \int\limits^a_b {f(x) \sqrt{1+ [f'(x)]^2}} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle y = \frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}\\Interval: [0, \frac{1}{3}][/tex]

Step 2: Differentiate

Basic Power Rule:                    [tex]\displaystyle y' = \frac{1}{2} \cdot \frac{1}{3}x^{\frac{1}{2} - 1} - \frac{3}{2} \cdot x^{\frac{3}{2} - 1}[/tex][Derivative] Simplify:                [tex]\displaystyle y' = \frac{1}{6}x^{\frac{-1}{2}} - \frac{3}{2}x^{\frac{1}{2}}[/tex][Derivative] Simplify:                [tex]\displaystyle y' = \frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}[/tex]

Step 3: Integrate Pt. 1

Substitute [Surface Area]:                                                                             [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{1+ [\frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}]^2}} \, dx[/tex][Integral - √Radical] Expand/Add:                                                               [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{81x^2+18x+1}{36x}} \, dx[/tex][Integral - √Radical] Factor:                                                                         [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{(9x + 1)^2}{36x}} \, dx[/tex][Integral - Simplify]:                                                                                       [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {-\frac{|9x + 1|(3x - 1)}{18}} \, dx[/tex][Integral] Integration Property:                                                                     [tex]\displaystyle SA = \frac{- \pi}{9} \int\limits^{\frac{1}{3}}_0 {|9x + 1|(3x - 1)} \, dx[/tex]

Step 4: Integrate Pt. 2

[Integral] Define:                                                                                             [tex]\displaystyle \int {|9x + 1|(3x - 1)} \, dx[/tex][Integral] Assumption of Positive/Correction Factors:                                 [tex]\displaystyle \frac{9x + 1}{|9x + 1|} \int {(9x + 1)(3x - 1)} \, dx[/tex][Integral] Expand - FOIL:                                                                                 [tex]\displaystyle \frac{9x + 1}{|9x + 1|} \int {27x^2 - 6x - 1} \, dx[/tex][Integral] Integrate - Basic Power Rule:                                                         [tex]\displaystyle \frac{9x + 1}{|9x + 1|} (9x^3 - 3x^2 - x)[/tex][Expression] Multiply:                                                                                      [tex]\displaystyle \frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|}[/tex]

Step 5: Integrate Pt. 3

[Integral] Substitute/Integral - FTC:                                                              [tex]\displaystyle SA = \frac{- \pi}{9} (\frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|})|\limits_{0}^{\frac{1}{3}}[/tex][Integrate] Evaluate FTC:                                                                                [tex]\displaystyle SA = \frac{- \pi}{9} (\frac{-1}{3})[/tex][Expression] Multiply:                                                                                     [tex]\displaystyle SA = \frac{\pi}{27} \ ft^2[/tex]

It is in ft² because it is given that our axis are in ft.

Step 6: Find Amount of Glass

Convert ft² to in² and multiply by 0.015 in (given) to find amount of glass.

Convert ft² to in²:                    [tex]\displaystyle \frac{\pi}{27} \ ft^2 \ \div 144 \ in^2/ft^2 = \frac{16 \pi}{3} \ in^2[/tex]Multiply:                                   [tex]\displaystyle \frac{16 \pi}{3} \ in^2 \cdot 0.015 \ in = 0.251327 \ in. \ of \ glass[/tex]

And we have our final answer! Hope this helped on your Calc BC journey!

This table represents the relationship between m, the amount of
money an employee has in the morning, and p, the amount of
money an employee has later in the day after they receive their
paycheck.
Which equation represents the relationship in the table?

a) p=m-160.25

b) p=160.25-m

c)p=m+160.25

d)p=200.25m+160.25

Answers

Answer:

bB

Step-by-step explanation:

The correct equation which represents the relationship in the table is,

⇒ p = m + 160.25

Where, m, the amount of money an employee has in the morning, and p, the amount of money an employee has later in the day after they receive their paycheck.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

This table represents the relationship between m, the amount of money an employee has in the morning, and p, the amount of money an employee has later in the day after they receive their paycheck.

Hence, By all options, we can check by substitute the given values.

So, By option 3;

The equation is,

⇒ p = m + 160.25

Substitute m = 200.25,

⇒ p = 200.25 + 160.25

⇒ p = 360.50

Thus, The correct equation which represents the relationship in the table is,

⇒ p = m + 160.25

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

i need help plssssssssssssss

Answers

Answer:

It doesn't show what the drop down is. However, both of those are linear expressions.

Sergio's expressionn siplifies to: 9+3x (because two minuses cancel each other).

Leon's expression cancels to 12+6x (because 9+3=12)

Step-by-step explanation:

You have to show the dropdown to be able to answer exactly what they are looking for as an answer.

The volume of a golf ball is approximately 4in.3 what is the diameter round you answer to the nearest whole number

A 4 in
B 6 in
C 1 in
D 2 in

Answers

Answer:

D. 2 inches.

Step-by-step explanation:

Given the following data;

Volume of golf (sphere) = 4 in³

A golf ball is spherical in shape. Thus, to find its volume we would use the formula for the volume of a sphere.

[tex] Volume \; of \; a \; sphere = \frac {4}{3} \pi r^{3} [/tex]

Substituting into the equation, we have;

[tex] 4 = \frac {4}{3} * 3.142* r^{3} [/tex]

Cross-multiplying, we have;

[tex] 12 = 4 * 3.142* r^{3} [/tex]

[tex] 12 = 12.568 * r^{3} [/tex]

[tex] r^{3} = \frac {12.568}{12} [/tex]

[tex] r^{3} = 1.0473 [/tex]

Taking the cube root of both sides, we have;

Radius, r = 1.016 inches.

To find the diameter;

Diameter = radius * 2

Diameter = 1.016 * 2

Diameter = 2.03 ≈ 2 inches.

Answer:

the answer is 2.

Step-by-step explanation:

i just did this question on the exam

Please I need help this is already late

Answers

the first would be A and hopes this helps


The two triangles shown are similar. Find the value of b.

Answers

Answer:

Since the corresponding sides of similar triangles are proportional,

[tex]\frac{a}{b}= \frac{2.1}{1.4} =\frac{3}{2}[/tex]

ANSWER FOR BRAINLIEST

Answers

Answer:

x = 10

Step-by-step explanation:

( 6x - 6 ) + ( 7x + 1 ) + 55 = 180

6x + 7x = 180 + 6 - 1 - 55

13x = 130

x = 10

Check:

6(10) - 6 = 56

7(10) - 1 = 69

55 + 56 + 69 = 180 ✔️

PLEASE DUE IN 20 MINUTES!!!!!!


Write the quadratic function in standard form.
f(x) = (x + 14)2

Answers

Answer:

Step-by-step explanation:

It's essential that you use the symbol " ^ " to indicate exponentiation.

Expanding f(x) = (x + 14)^2 results in x^2 + 28x + 196 (which is in standard form)

PLZ ANSWER QUICK IT WILL HELP A LOT!

Answers

Answer:

A

Step-by-step explanation:

i believe it’s A!!!!!!!!!!!

Calculate or Simplify the value of each expression a {-8} . 2/3

Answers

Answer:

Step-by-step explanation:

[tex](-8)*\frac{2}{3}=\frrac{(-8)*2}{3}= \frac{-16}{3}[/tex]

what does 40 centimeters equals in meters

Answers

Answer:

Its 0.4 meters!

Step-by-step explanation:

What is the image of the point (8,-6)(8,−6) after a rotation of 180 counterclockwise about the origin?

Answers

Answer:

(-8, 6)(-8, 6)

Step-by-step explanation:

The formula for 180 degree rotation is (-x, -y)

A mechanic charges $20.00 an hour, h for labor plus parts. If the parts cost $217.00, write a linear equation that will find the total cost, c. ​

Answers

Answer:

y=20x+217

Step-by-step explanation:

5/8^3+9-1/4^3= I really need help!!!

Answers

Answer: 3/8q^3 + 9

Step-by-step explanation:

1. combine like terms 5/8q^3 - 1/4q^3, need to make denominator the same to subtract so multiply 2/2 by 1/4q^3, 5/8q^3 - 2/8q^3 = 3/8q^3

2. final answer is : 3/8q^3 + 9

Math equation with its graph

a) y=3x+2

b) y= -x+5

c) y= 2x-1

d) y= -4x

See picture attached

Please help

Answers

Answer:

y=3x+2 to B

y=-x+5 to D

y=2x-1 to C

y=-4x to A

Solve the system of equations by Linear Combination (Elimination)
6x - 2y = 16
x + 2y = 5
a) (3,1)
b) (1,3)
c) Infinite Many Solutions
d) No Solution
PLEASE PLEASE PLEASE HELPPP MEEE

Answers

Let me know if you have any questions!

what is the answer to 4x+10=26

Answers

the correct answer is x= 4

Answer:

x=4

Step-by-step explanation:

4x+10=26

Subtract 10 from both sides

4x=16

Divide by 4

x=4

Hey Everyone I was asking anyone can help with this problem it would really appreciated.

Answers

Answer:

angle G = angle I

HGI=HIJ by RHS fact

HGI=HIJ corresponding angles are alwyas congurrent

25. Explain the Error Jeremy factored 144x? – 100 as follows:
144x2 100 = (12x + 10)(12x – 10)
= 2(6x + 5)(6x – 5)
What was his error? Correct his work.

Answers

Given:

Consider the expression is

[tex]144x^2-100[/tex]

Jeremy factored the given expression and his steps are given.

To find:

The error in his solution.

Solution:

We have,

[tex]144x^2-100[/tex]

It can be written as

[tex]=12^2x^2-10^2[/tex]

[tex]=(12x)^2-10^2[/tex]

[tex]=(12x+10)(12x-10)[/tex]             [tex][\because a^2-b^2=(a+b)(a-b)][/tex]

Taking out common factors from each parenthesis.

[tex]=2(6x+5)2(6x-5)[/tex]

[tex]=4(6x+5)(6x-5)[/tex]

So, Jeremy was incorrect because the common factor is [tex]2\times 2=4[/tex] instead of 2.

Therefore, Jeremy made his mistake in his last step.

n the rectangle P Q R S , the side P Q is of length 2 and the side Q R is of length 4

Please i need the answer ASAP

Answers

here u go

In the rectangle PQRS , the side PQ is of length 2CM and the side QR is of length 4CM Points  T and  U  lie inside the rectangle so that Triangle PQT and TRIANGLE RSU are equilateral triangles.

PLS MARK ME AS BRAINLIST!!!!!

Kate has 48 softballs. She wants to divide them evenly among b softball bags. Which expression represents how many softballs she should put into each bag?

Answers

Answer:

Softballs = (48/b)

Step-by-step explanation:

Given that,

Total number of softballs = 48

She wants to divide them evenly among b softball bags.

We need to find an expression that represents how many softballs she should put into each bag.

As it is dividing among b softball, it means we divide 48 and b. So,

[tex]s=\dfrac{48}{b}[/tex]

Hence, the required expression is (48/b).

Division as Fractions - Word
Name
cach problem. Make sure to write your answer as a fraction.
Henry wanted to collect 65 pounds of cans in 7 days. How much should he
collect each day to reach his goal? Which two whole numbers does your
answer lie between?

Answers

Answer:

65/7

=9.28..lies btwn 9 and 10

Step-by-step explanation:

You want to add lace around the outside of your circular kitchen table cloth. If the diameter of the table cloth is 16 cm, then which of the following measurements would represent how much lace you need?

Answers

The length of lace would be the circumference of the circle.

Circumference = diameter x Pi

Circumference = 16pi cm

Circumference = 50.24 cm ( approximately)

Answer:

The circumference of the circle.

Step-by-step explanation:

Other Questions
Please calculate the energy stored in a flying wheel. The steel flying wheel is 10 metric tons, in adiameter of 10m, and it rotates at a speed of 1000 rpm. The steel density is 8050 kg/m^3. When energyis fully released, the flying wheel stops its rotation. What is the area, in square feet, of the rectangle shown below? Pina Colada Corp. issued 22000 shares of $1 par common stock for $40 per share during 2022. The company paid dividends of $53000 and issued long-term notes payable of $484000 during the year. What amount of cash flows from financing activities will be reported on the statement of cash flows PART B: Which detail from the texts best supports the answer to Part A?A. An eclipse takes place when one heavenly body such as a moon orplanet moves into the shadow of another heavenly body." (Paragraph 1)B. "A lunar eclipse usually lasts for a few hours. At least two partial lunareclipses happen every year, but total lunar eclipses are rare. It is safeto look at a lunar eclipse." ( Paragraph 6)C. "NEVER look directly at the sun: It can permanently damage youreyes! You must use proper safety equipment to look at any type ofsolar eclipse." ( Paragraph 14)D. "This path, where the moon will completely cover the sun so the sun'scorona can be seen, will stretch from Salem, Oregon, to Charleston,South Carolina." ( Paragraph 17)Science What IS Imperialism I am CONFUSHION a\large 140\frac{1}{2} b\large 140\frac{1}{3} c\large 141 d\large 140\frac{3}{4} again I'm asking this question only answer it if u KNOW. I don't need information of the war it's just ur point if view. consider the causes, the cost; and the impact of the war. do you consider this war was worth fighting? explain. by the way I'm talking about war of 1812 if u don't know the answer please let someone else answer it Why does agriculture thrive in the Delta-Yazoo region?The region is full of dense pine forests.The region has swampy land and good soil.The region has a lot of fertile loess soil.The region is full of sandy beaches. Most people in southwest Asia practice which religion?A. JudaisimB. BuddhismC. IslamD.Christianity Two objects travel the same distance. The one that is moving faster will:Take more time to go the distanceTake less time to go the same distanceTake the same time as the slower objectNone of the above The random module is a group of functions that are used to deal with random numbers.TrueFalse 1. Evaluate the expression for the given value of the variable. 4(z+ 4) + 5 for z = 2A 4(2z + 4) +5B -3C 17D 29 A bag weighing 20 N is pushed horizontally a distance of 35 m across alevel floor by a force of 10 N, How much work is done on the bag inJoules? W=Fd * The next number in the arithmetic sequence 10, 23, 36, __is:49.46.43.50. As a person pushes a box across a floor, the energy from the person's moving arm is transferred to the box, and the box and the floor becomes warm. During the process, what happens to energy Expression 10 x (250 + 45) years A beachfront hotel is planning for its summer busy season. It wishes to estimate with 95% confidence the average number of nights each guest will stay in a single visit. Using a sample of guests who stayed last year, the average number of nights per guest is calculated at 5 nights. The standard deviation of the sample is 1.5 nights. The size of the sample used is 120 guests and the beachfront hotel desires a precision of plus or minus 0.5 nights.Required:a. What is the standard error of the mean in the lakefront resort example? b. Within what range below can the resort expect with 95% confidence for the true population mean to fall? Which phrase best defines the Holocaust?A The U.S. plan to relocate Japanese Americans to internment campsB The Allied plan to liberate concentration camps in Eastern EuropeC The Nazi campaign to use genocide to eliminate European JewsD The Japanese military strategy to destroy U.S. aircraft carriers According to the Michaelis-Menten equation, when an enzyme is combined with a substrate of concentration s (in millimolars), the reaction rate (in micromolars/min) is What is the rebuttal in an argumentative essay?