Find a formula for the exponential function passing through the points
4
3,
and (1,20)
125
f(x) -

Find A Formula For The Exponential Function Passing Through The Points43,and (1,20)125f(x) -

Answers

Answer 1

Answer:

[tex]y = 4*5^x[/tex]

Step-by-step explanation:

Given

[tex](x_1,y_1) = (-3,\frac{4}{125})[/tex]

[tex](x_2,y_2) = (1,20)[/tex]

Required

Determine the exponential equation

An exponential equation is of the form: [tex]y = ab^x[/tex]

In: [tex](x_2,y_2) = (1,20)[/tex]

[tex]20 = ab^1[/tex]

[tex]20 = ab[/tex] ---- (1)

In: [tex](x_1,y_1) = (-3,\frac{4}{125})[/tex]

[tex]\frac{4}{125} = ab^{-3}[/tex] --- (2)

Divide (1) by (2)

[tex]20/\frac{4}{125} = \frac{ab}{ab^{-3}}[/tex]

[tex]20/\frac{4}{125} = b^4[/tex]

[tex]20*\frac{125}{4} = b^4[/tex]

[tex]5*125 = b^4[/tex]

[tex]625 = b^4[/tex]

Take 4th roots of both sides

[tex]\sqrt[4]{625} = b[/tex]

[tex]5 = b[/tex]

[tex]b = 5[/tex]

Substitute [tex]b = 5[/tex] in [tex]20 = ab[/tex]

[tex]20 = a * 5[/tex]

Solve for a

[tex]a = 20/5[/tex]

[tex]a = 4[/tex]

Hence, the equation is:

[tex]y = 4*5^x[/tex]


Related Questions

Consider the equation below.



Determine which equation has the same solutions as the given equation.

Answers

Answer:

A) (x - 5)² = 36

Step-by-step explanation:

x² - 10x - 11 = 0

A) CORRECT

(x - 5)² = 36

x² - 10x + 25 = 36

x² - 10x + 25 - 36 = 0

x² - 10x - 11 = 0

The chemical element einsteinium -253 naturally loses its mass over time . A sample of einsteinium-253 had an initial mass of 320 grams when we measured it. The relationship between the elapsed t, in days, and the mass,m(t), in grams left in the sample is modeled by the following function: M(t)=320•(0.125)^t/61.4 complete the sentence: the sample loses 87.5% of its mass every ___ days.

Answers

Answer: 61.4

Step-by-step explanation:

Can someone please answer this

Answers

Answer:

sorry bro i need points i got 10 minutes left on dis quiz but i recommond course hero bro have a good day

Step-by-step explanation:

I need help with 7-9 please

Answers

9514 1404 393

Answer:

  7.  4 cm

  8.  206 paper cups

  9.  175pi cm³

Step-by-step explanation:

7. The formula for the volume of a cone can be used.

  V = 1/3πr²h

  h = 3V/(πr²) = 3(48π cm³)/(π(6 cm)²) = 144/36 cm = 4 cm

The height of the cone is 4 cm.

__

8. The volume of the cone with the given dimensions is ...

  V = 1/3π(4 cm)²(11 cm) = 176/3π cm³ ≈ 184.307 cm³

The number of times this volume can be filled by 10 gallons is ...

  (10 gal)(3785 cm³/gal)/(184.307 cm³/cup) = 205.3 cups

206 paper cups are needed.

__

9. We know from the formula for the volume of a cone that it has the same volume as a cylinder 1/3 its height. The composite figure is equivalent to a cylinder with a height of ...

  3 cm +(12 cm)/3 = 7 cm

Then the volume is ...

  V = πr²h

  V = π(5 cm)²(7 cm) = 175π cm³

__

For this, we recognize that the triangle with sides h, 5, and 13 will be a 5-12-13 right triangle, so the height of the conical part of the figure is h=12 cm. If you haven't remembered that Pythagorean triple, you can find the height from the Pythagorean theorem:

  h² +5² = 13²

  h = √(169 -25) = √144 = 12

8ftx4ftx5ft what is the diameter

Answers

Answer:

nothing

Step-by-step explanation:

Find the indicated side of the
right triangle
60°
7
30°
х
X=
= [?] )

Answers

The value of x is 14 units.

Trigonometry values

When handling and dealing with difficulties involving the measurement of length and angles of a right-angled triangle, trigonometric values of ratios such as sine, cos, tan, cosec, cot, and secant come in handy. The trigonometric function is widely used to solve trigonometric issues at 0°, 30°, 45°, 60°, and 90°.

How to determine value of x?

We know for angle of 30° the base is 7 and perpendicular is x

then

sin30° = 7/x

      [tex]\frac{1}{2} =\frac{7}{x}[/tex]

       x = 7

hence, the value of x = 14 units

Learn more about Trigonometry values here: https://brainly.com/question/22698523

#SPJ2

please help me
A book is marked 21% off. If the original price is $23.42, what will the sale price be?

Round your answer to the nearest cent. Do not include units with your answer.

Answers

Answer:

$18.51

Step-by-step explanation:

23.42×.21= 4.91 then 23.42-4.91= your sale price which is $18.51

The courtyard outside East Middle School is in the shape of a rectangle and half-circle.
What is the approximate area of the courtyard?

Answers

Answer:

The correct option is the third one counting from the top. (5892 m^2)

Step-by-step explanation:

First, we need to remember that:

For a rectangle of length L and width W, the area is:

A = L*W

For a circle of diameter D, the area is:

A = pi*(D/2)^2

Where pi = 3.14

In the image, we can see a rectangle and half a circle, the total area of the image will be equal to the area of the rectangle plus the area of the half circle.

In the image, we can see a rectangle of length L = 100m and width W = 50m

Then the area of the rectangle is:

A = 100m*50m = 5000m^2

And we can see that for the half-circle the diameter is D = 50m

Note that the area of a half-circle is half of the area of a complete circle, then the area of that half-circle is:

A = (1/2)*(3.14*(50m/2)^2) = 981.25 m^2

If we add these two areas we get:

Total area =  5000m^2 + 981.25 m^2 = 5981.25 m^2

If we round it up, we get:

Total area = 5982 m^2

The correct option is the third one counting from the top.

Consider two matrices, A and B

To do the operation shown, which statements must be true about Matrix A and Matrix B?

AxB

A. The number of columns in Matrix A must equal the number of rows in Matrix B

B. The number of rows in Matrix A must equal the number of columns in Matrix B

C. The number of rows in Matrix A must equal the number of rows in matrix B

D. The number of columns in Matrix A must equal the number of columns the matrix B

Answers

A. The number of columns in Matrix A must equal the number of rows in Matrix B

Neil swam 4 2/3 lengths of the pool. Mia swam 6 1/2 lengths of the pool. How many more lengths did Mia swim than Neil

Answers

Answer:

1 5/6

Step-by-step explanation:

find the value of x ....

Answers

Answer:

C

Step-by-step explanation:

3x-9+30+24=180

3x+45=180

3x=135

x=45

Can someone help me pls I’m stuck

Answers

Answer:

∠A = 53.58°

Step-by-step explanation:

cos A = 19/32 = 0.5938

∠A = 53.58°

Find g(-6) when g(x)
= x+3/x-1

Answers

Answer: The answer would be 3/7.

Step-by-step explanation:


PLEASE SOMEONE HELP I WILL GIVE BRAINLIEST
(Look at the picture)

Answers

X=12 because the ABC triangle is doubled the values

The similarity ratio of two similar triangles is equal to the ratio of their corresponding sides :

Similarity ratio = BA / GF = BC / GH = CA / HF

Similarity ratio = 18 / 9 = 14 / 7 = x / 6

x / 6 = 2

multiple sides by 6

6 × x / 6 = 6 × 2

simplification

x = 12

No LINK Easy math please help is this liner y=2\x +1 explain please too

Answers

Answer:

It is not linear

Step-by-step explanation:

If you plug that function into Desmos graphing Calculator, you can see there are two leparate lines and they are not straight.

please please help!!

Answers

Answer:

A family buys 6 tickets to a show. they also pay a $3 parking fee. they spend $27 total.

Find the area of the parallelogram

Answers

Answer: 621 cm

A = bh

A = 27 x 23

A = 621

What is the approximate surface area of the Hayden Sphere in terms of T?
4731 ft?
37857 ft?
75697 ft2
18927 ft?

Answers

Answer:

[tex]A=7569\pi \ ft^2[/tex]

Step-by-step explanation:

The diameter of a sphere is 87 feet.

We need to find its surface area. The formula for surface area is given by :

[tex]A=4\pi r^2[/tex]

Where

r is the radius of the sphere

[tex]A=4\pi \times (\dfrac{87}{2})^2\\\\=7569\pi \ ft^2[/tex]

So, the surface area of the sphere is equal to [tex]7569\pi \ ft^2[/tex].

12/23 plus -11/23 e eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

1/23

Step-by-step explanation:

This honestly super easy, but here it is!

12/23+(-11/23)

With no negatives, it would be 12/23+11/23 and the answer would be 23/23 AKA 1, because 12+11=23.

With negatives though, you always have to subtract the number itself from the positive number if the number is negative. Here we will subtract 11 from 12, which brings us to 1/23.

Hope this helped!

I wouldn't mind a 5-star rating, a thanks, or even a Brainliest :D

-ChocoChocoCho

how did they get that answer? please answer

Answers

Answer:

Look at my explanation

Step-by-step explanation:

The circumference of a circle is 2πr, so you can set it up like this since the circumference was 22π.

2πr = 22π

divide both sides by 2

πr = 11π

divide both sides by π

you get r = 11

So your radius is 11.

To find the area, you must do πr^2 ("^2" means squared)

if you substitute 11 for r you get

11π^2

you can do 11 squared first

11^2 = 121

the area of the circle = 121π

Keep in mind that they said to use 3.14 for π

so you can do 121 x 3.14

Final Answer: 379.94

Simplify 5x + 4x + 1. ​

Answers

Answer:

9x + 1

Step-by-step explanation:

Combine like terms. Like terms are terms with the same amount of the same variables.

Add 5x and 4x:

5x + 4x + 1

(5x + 4x) + 1

9x + 1

9x + 1 is your answer.

~

I need to help me with this problem I'm not sure what I'm supposed to do.
Consider a point with rectangular coordinates (x,y).
If x<0 then the polar coordinates of the point are (r,θ) where r≥0 and −π/2≤θ<3π/2and:

r=

θ=

If x≥0 then the polar coordinates of the point are (r,θ) where r≥0 and −π/2≤θ<3π/2 and:

r=

θ=​​

Answers

Answer:

1.24

Step-by-step explanation:

i subtracted 1-1

I don’t know how to do this I just want gains point

HELP ASAP!!!! 20 POINTS!!

Answers

Answer:

Can you upload this as a jpg, I can't open it to asnwer. Also, you listed 10 points not 20.

Step-by-step explanation:

whcich expression are equivialant to the one below 3^4*3^x

Answers

Answer:

3x+4

Step-by-step explanation:

Find the dot product of vectors u = -4i + 7j and v = 2i + j

Answers

Answer:

The desired dot product is -1

Step-by-step explanation:

To find the dot product of the given vectors, multiply the magnitudes of the 'i' and 'j' terms together, separately, and then add the results:

dot product of u and v = (-4)(2) + (7)(1) = -8 + 7 = -1

The desired dot product is -1

3
An animal shelter spends $2.35 per day to care for each cat and $5.50 per day to
each dog. Pat noticed that the shelter spent $89.50 caring for cats and dogs on W
Pat found a record showing that there were a total of 22 cats and dogs at the she
Wednesday. How many cats were at the shelter on Wednesday?
22.
I’m

Answers

Answer:

10 cats were at the shelter on wednesday

Step-by-step explanation:

I need help I will mark you

Answers

Answer:

the answer is D, 30% of his budget is spent on clothes

please answer the attached question.

Answers

Answer : fx + fh - f(x) / h

8. Daren and Josh are pretty good free throw shooters. Daren makes 75% of the
free throws he attempts. Josh makes 80% of his free throws. Suppose we take
separate random samples of 50 free throws each from Daren and Josh, and
record the proportion of free throws that are made by each. Which of the
following best describes the sampling distribution of PD - Pj?

Answers

Answer:

B) Approximately normal, with mean -0.05 and standard deviation 0.083

Step-by-step explanation:

The correct answer is (B). The shape is approximately normal since the expected number of makes and misses for both Daren and Josh are all greater than 10.

The distribution of pD = pJ is given by: Option B: Approximately normal, with mean -0.05 and standard deviation 0.083

What is the distribution of population proportion?

For large enough sample, let the population proportion of a quantity be denoted by random variable [tex]p[/tex]

Then, we get:

[tex]p \sim N(\hat{p}, \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}})[/tex]

where

[tex]\hat{p}[/tex] = estimated(mean value) proportion of that quantity, and n = size of sample drawn.
What is the distribution of random variable which is sum of normal distributions?

Suppose that a random variable X is formed by n mutually independent and normally distributed random variables such that:

[tex]X_i = N(\mu_i , \sigma^2_i) ; \: i = 1,2, \cdots, n[/tex]

And if

[tex]X = X_1 + X_2 + \cdots + X_n[/tex]

Then, its distribution is given as:

[tex]X \sim N(\mu_1 + \mu_2 + \cdots + \mu_n, \: \: \sigma^2_1 + \sigma^2_2 + \cdots + \sigma^2_n)[/tex]

Here, we're specified that:

For proportion of correct free throw attempts by Daren:

Sample size = n = 50Estimated proportion = [tex]\hat{p}_D = 75\% = 0.75[/tex]Let the population proportion be represented by variable [tex]p_D[/tex]

For proportion of correct free throw attempts by Josh:

Sample size = n = 50Estimated proportion = [tex]\hat{p}_J = 80\% = 0.8[/tex]Let the population proportion be represented by variable [tex]p_J[/tex]

And therefore, we have:

[tex]p_D \sim N\left (0.75, \sqrt{\dfrac{0.75 \times 0.25}{50}}\right )\\\\p_J \sim N\left (0.80, \sqrt{\dfrac{0.8 \times 0.2}{50}}\right )[/tex]

And therefore, we get:

[tex]-p_J \sim N\left (-0.80, \sqrt{\dfrac{0.8 \times 0.2}{50}}\right )[/tex] (standard deviation doesn't get affected by change of sign of the considered random variable, and mean gets affected linearly, so mean became negative 0.80 and standard deviation stays same).

Adding [tex]p_D[/tex] and [tex]-p_J[/tex], we get:

[tex]p_D + (-p_J) = p_D - p_j \sim N\left (0.75 -0.80, \sqrt{\dfrac{0.8 \times 0.2}{50} + \dfrac{0.75 \times 0.25}{50}}\right )\\\\p_D - p_J \sim N\left( -0.05, 0.0837\right)[/tex]

Thus, the distribution of pD = pJ is given by: Option B: Approximately normal, with mean -0.05 and standard deviation 0.083

Learn more about population proportion here:

https://brainly.com/question/7204089

PLEASE ANSWER ILL GIVE YOU BRAINLIEST

Answers

Answer:

It is 276.32

The equation is 2 times pi times radius times height, plus 2 times pi times radius squared.

r=radius

h=height

π=pi (3.14)

The radius is half the diameter and is given. It is 4.

The height is also given. It is 7.

So, follow GEMDAS and plug it in.

(2 x 3.14 x 4 x 7) + (2 x 3.14 x 4^2)

Plug it into the calculator and it will give you 276.32.

Hope this helps!

Have a great day and please rate and put thanks if it helped.

Also, if you can, mark me!

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