HELP! Determine the equation of the exponential function with a common ratio of 2, a horizontal asymptote at y = 4, and passing through the point (2, 10).

Answers

Answer 1

Answer:

[tex]\bold{y=1.5\times 2^x+4}[/tex]

Step-by-step explanation:

Equation for an exponential function is given as following:

[tex]y=ab^x+c[/tex]

Where b is the common ratio and  

c is the horizontal asymptote (y value)

a is the coefficient of exponential term of [tex]x[/tex]

[tex](x,y)[/tex] are the points on the function.

Here, we are given that:

Common ratio, b = 2

Horizontal asymptote at y, c = 4

So, the equation becomes (let us put the values of b and c):

[tex]y=a\times 2^x+4[/tex]

We need the value of a. Let us put value of (x,y) as (2,10).

[tex]10=a\times 2^2+4\\\Rightarrow a\times 4 =10-4 =6\\\Rightarrow a =\dfrac{6}{4} =\bold{1.5}[/tex]

So, the final equation of the exponential function is:

[tex]\bold{y=1.5\times 2^x+4}[/tex]


Related Questions

How to do this question plz answer my question step by step plzz plz plz plz ​

Answers

Answer:

40°, 95°, 105°, and 160°

Step-by-step explanation:

Let the smallest angle be x.

Measures of the 3 angles can be expressed as:

[tex] x + 55 [/tex]

[tex] x + 65 [/tex]

[tex] x + 120 [/tex]

The sum of all angles in a quadrilateral = 360°.

Therefore, [tex] (x + 55) + (x + 65) + (x + 120) = 360 [/tex]

Solve for x

[tex] x + 55 + x + 65 + x + 120 = 360 [/tex]

[tex] 3x + 240 = 360 [/tex]

[tex] 3x + 240 - 240 = 360 - 240 [/tex]

[tex] 3x = 120 [/tex]

[tex] \frac{3x}{3} = \frac{120}{3} [/tex]

[tex] x = 40 [/tex]

The smallest angle = 40°

Plug in the value of x in the earlier stated expressions to find the measure of the other angles:

[tex] x + 55 = 40 + 55 = 95 [/tex]

[tex] x + 65 = 40 + 65 = 105 [/tex]

[tex] x + 120 = 40 + 120 = 160 [/tex]

If 3x+2=7(3-x), find the value of 26-x-4

Answers

Answer:

           20.1

Step-by-step explanation:

3x + 2 = 7(3 - x)

3x + 2 = 21 - 7x

3x + 7x = 21 - 2

10x = 19

 x = 1.9

[tex]26-x-4 = 26 - 1.9 -4 = 20.1[/tex]

Sean runs 5 miles North of his house and then runs 3 miles East of his house. What is his displacement?

Answers

Answer: 5.83 milea

Step-by-step explanation:

As displacement is the shortest distance between two points. Now 5 miles north and 3 miles east so it makes a Right angle traingle and the hypotenuse is the displacement so

Displacement is (5^2 +3^2)^0.5 =5.83 miles.

The displacement is 5.83 miles.

What is a Triangle?

A triangle in geometry is a three-sided polygon with three edges and three vertices.

As per the given data:

Miles Sean ran to the north of his house = 5 miles

Miles Sean ran to the east of his house = 3 miles

For finding the displacement, we have to find out the length of the line from the initial to the final position of Sean.

As Sean first ran north and then ran east, a right-angled triangle is made.

The displacement of Sean is given by the hypotenuse of this right-angled triangle.

The perpendicular is the distance ran in north.

The base is the distance ran in east.

Now, by using the Pythagoras theorem:

H² = P² + B²

H² = (5)² + (3)²

H² = 25 + 9

H² = 34

H = √34 = 5.83 miles

The displacement is 5.83 miles.

Hence, The displacement is 5.83 miles.

To learn more on Triangle, click:

brainly.com/question/19976619

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Janet wants to calculate the time it takes to earn a certain amount of
interest on a principal amount in an investment with simple interest. What
equation can she use?

Answers

Answer:

The time it takes to earn an amount A with a given principal P invested for a time period t is t = (A/P - 1)/r

Step-by-step explanation:

In order to calculate the time it would take to earn a certain amount of interest on a principal amount in an investment with simple interest, we use the simple interest formula as follows;

A = P·(1  + r·t)

A = The final amount after the number of periods of investment

P = The principal or initial amount

r = The interest rate per period

t = The number of the time periods

Therefore, the time it takes to earn a certain amount of interest on a principal amount in an investment with simple interest is fount by making t the subject  of the above equation, which is given as follows;

A/P = 1 + rt

rt = A/P - 1

t = (A/P - 1)/r

Therefore, the time it takes to earn an amount A with a given principal P invested for a time period t is given by t = (A/P - 1)/r.

Which term does not belong with the other three?


AB¯¯¯¯¯¯¯¯

plane CDE

FG←→

HI−→

Question 2
Explain your reasoning.


The one that does not belong is an undefined term.

The one that does not belong uses a different kind of symbol.

The one that does not belong contains fewer points.

The one that does not belong has a different number of dimensions.

Answers

Answer:

The one that does not belong has a different number of dimensions.

Step-by-step explanation:

Given list consists of:

a line segment (AB)a plane (CDE)a line (FG)a ray (HI)

Three of them have one dimension but the plane has two dimensions,

therefore the plane in the list does not belong with the other three.

So correct answer choice is:

The one that does not belong has a different number of dimensions.

Please solve 5x = 75

Answers

Answer:

x=15

Step-by-step explanation:

5x= 75 (divide)

75/5= 15

Answer: There is only one step to solve this equation; we use inverse operations to isolate the x by dividing 5 on both sides. We divide because 5 is being multiplied by x, and the inverse operation for multiplication is division.

5x/5 = x

75/5 = 15

The equation now looks like:

x = 15

x is equal to 15. This is your answer.

what is 28x +25x +23x+23x+45x+1234890x+6389x+1783x=?????

Answers

Answer:

1,243,206x

Step-by-step explanation:

Combine like terms:

[tex]28x +25x +23x+23x+45x+1234890x+6389x+1783x\\\\=\boxed{1243206x}[/tex]

The expression can no longer be simplified.

All Parent functions have both x- intercepts and y-intercepts EXCEPT. I. Linear II. Absolute Value III.Quadratic IV. Cubic V.Square root VI. Cube root VII. Reciprocal VIII. Exponential IX. Logarithmic

Answers

Answer:

Reciprocal, Exponential and Logarithmic.

Step-by-step explanation:

x intercept is the value of x where y value is 0.

y intercept is the value of y where x value is 0.

Let us have a look at the possibility for each parent function as given.

I. Linear

[tex]y =x[/tex]

When x = 0, y = 0 and

When y = 0, x = 0

Therefore, both x and y intercept exist.

II. Absolute value

[tex]y =|x|[/tex]

When x = 0, y = 0 and

When y = 0, x = 0

Therefore, both x and y intercept exist.

III. Quadratic

[tex]y =x^{2}[/tex]

When x = 0, y = 0 and

When y = 0, x = 0

Therefore, both x and y intercept exist.

IV. Cubic

[tex]y =x^3[/tex]

When x = 0, y = 0 and

When y = 0, x = 0

Therefore, both x and y intercept exist.

V. Square root

[tex]y =\sqrt x[/tex]

When x = 0, y = 0 and

When y = 0, x = 0

Therefore, both x and y intercept exist.

VI. Cube root

[tex]y =\sqrt[3]x[/tex]

When x = 0, y = 0 and

When y = 0, x = 0

Therefore, both x and y intercept exist.

VII. Reciprocal

[tex]y =\dfrac{1}x[/tex]

When [tex]x = 0, y \rightarrow \infty[/tex]

Therefore, both x and y intercept do not exist.

VIII. Exponential

[tex]y =b^x[/tex]

where b is any base:

When [tex]x = 0, y =1[/tex] therefore y intercept exists.

When we put y = 0, which is not possible

Therefore, both x and y intercept do not exist.

IX. Logarithmic

[tex]y =logx[/tex]

When [tex]x = 0, y \rightarrow[/tex] not defined

Therefore, both x and y intercept do not exist.

Example 1: Simplify the expression,
127 - 2(3+4)

Answers

Answer:

113

Step-by-step explanation:

127 - 2(3+4)

127 - 2(7)

127-14

113

Let ABCD be a parallelogram such that AB = 10 , BC = 14, and Angle A = 45. Find the area of the parallelogram. Please do not answer in decimal form. Answer using a square root

Answers

Answer:

70√2  units²

Step-by-step explanation:

(see attached for reference notes on parallelograms)

we are given ABCD is a parallelogram where

Short Length, AB = 10 units

Long Length, BC = 14 units

Angle A = 45°

The area of the parallelogram is hence,  

= AB x BC sin 45°

= 10 x 14 x sin 45

= 140 sin 45°    (recall from special angles, that sin 45° = 1/√2)

= 140/√2   (remove radical from denominator by multiplying by √2/√2)

= (140/√2) x (√2/√2)

=70√2  units²

Express 16 as a product of its prime factors.

Answers

Answer:

16 = 1 x 16, 2 x 8, or 4 x 4. Factors of 16: 1, 2, 4, 8, 16. Prime factorization: 16 = 2 x 2 x 2 x 2,

Step-by-step explanation:

which can also be written 16 = 2⁴. Since √16 = 4, a whole number, 16 is a perfect square

if this helped please give me brainliest

Answer:

It will be:

Step-by-step explanation:

16=:

a) 1 x 16

b) 2 x 8

c) 4 x 4

All these are the product of 16 prime factors.

Prime factors are any of the number that can be multiplied to give the original number.

Hope they help.

b. Is the a discrete random variable, a continuous random variable, or not a random variable? time it takes for a light bulb to burn out A. It is a discrete random variable. B. It is a continuous random variable. C. It is not a random variable

Answers

Answer:

The correct answer is:

It is a continuous random variable (C)

Step-by-step explanation:

Continuous Random Variables are variables that do not take on a distinct value. They take on values that are a range of different possibilities to infinity. In continuous random variables, the values cannot be counted. In this example, the time it takes for a light bulb to burn out can be any rational number which is greater than 0, up to infinity; for instance, it can be 24 hours, 24.5 hours, 30.8 hours, 51.2 hours etc. There is an infinite possibility of the time it takes for the bulb to burn out.

Discrete Random Variables are ones in which the variables take on distinct values and nothing in between. Here, the outcomes can be counted. For example if a coin is tossed, there are only two possibilities which can be the outcome and that is either head, or tail. The number of possible outcome is 2, and there is nothing inbetween head or tail.

Answer:

It’s C

(Gibberish words to so i can to 29 words)

hciejdgrifgirgrittrufifgeydifufgfidhfuvifgdudugcudydgdidhdhf

Hope this helped,if not, don’t hate.

Someone please help me with this question I need it ASAP

Answers

Your question has been heard loud and clear.

First one (x+2i)(x-2i) = x^2+4

Second one (x-2+2i)(x-2-2i) = x^2-4x+8

Third one (x+1+i)(x+1-i) = x^2+2x+2

Thank you

Edit: Sorry for taking 15 minutes I was calculating lol

What makes the equation true?
4(-x+2) = -(x+3) - 2x

Answers

Answer:

x=11

Step-by-step explanation:

The fact of x=11 makes the equation true as for if it didnt work correctly it wouldnt be true.

What is y=1/2x+4 in standard form?

Answers

Answer:  x-2y = -8

===========================================

Explanation:

Multiply both sides by 2 to clear out the fraction

y = (1/2)x+4

2y = 2[ (1/2)x + 4 ]

2y = 2*(1/2)x + 2*4

2y = x + 8

Then move the x term over to the left side

2y = x+8

2y-x = 8

-x+2y = 8

Optionally we can multiply both sides by -1

-x+2y = 8

-1*(-x+2y) = -1*8

x-2y = -8

This is in standard form Ax+By = C with A = 1, B = -2, C = -8

The reason why I multiplied both sides by -1 was to make A > 0 which is what some textbooks use as convention. Of course -x+2y = 8 is equally valid too.

Lin deposited $300 in a savings account that has a 2% interest rate per year. How much is in her account after 1 year? After 2 years? Diego wants to sell his bicycle. It cost $150 when he bought it but has depreciated by 15%. How much should he sell it for? I will give brainlyies

Answers

Answer:

Step-by-step explanation:

Lin after 1 year has 300+2*300/100=300+6=306  $

     after 2 years has 306+2*306/100=306+6.12=312.12$

150-15*150/100=150-22.5=127.5 $ the price for the bicycle

The value after 20 years is $ 723.514

Solution:

Formula for Amount compounded annually is as follows:  

Where,

"A" is the total amount

"p" is the principal sum

"r" is the rate of interest

"n" is the number of years

From given question,

p = $ 300

r = 4.5 %

n = 20 years

Substituting the values we get,

Thus value after 20 years is $ 723.514

PART 2)

2. Given data

Cost of bicycle = $150

Depreciation = 15%

Firstly let us calculate 15% of $150

(15/100)*150 =0.15*150

= $22.5

Since the value depreciated

We will minus the the depression from the initial amount

New amount = 150-22.5=

$127.5

AC = 22, BC = x + 14, and AB = x + 10.
Find x.​

Answers

Hi there! :)

Answer:

[tex]\huge\boxed{x = -1}[/tex]

Given:

AC = 22

BC = x + 14

AB + x + 10

AC is equivalent to AB + BC, therefore:

AC = AB + BC

Substitute in the expressions:

22 = (x + 10) + (x + 14)

Combine like terms:

22 = 2x + 24

Subtract 24 from both sides:

-2 = 2x

Divide both sides by 2:

x = -1

Given : AC = 22, BC = x + 14, and AB = x + 10.

[tex]\rule{130}1[/tex]

Solution :

[tex]:\implies\sf AB + BC = AC\:\:\:\:\Bigg\lgroup \bf{Segment\: addition\: postulate}\Bigg\rgroup \\\\\\:\implies\sf (x + 10) + (x + 14) = 22\:\:\:\:\Bigg\lgroup \bf{Substitution}\Bigg\rgroup\\\\\\:\implies\sf 2x + 24 = 22\:\:\:\:\Bigg\lgroup \bf{Simplify\:(added\:like\:term)}\Bigg\rgroup\\\\\\:\implies\sf 2x = -2\\\\\\:\implies\sf x = \dfrac{-2}{2}\\\\\\:\implies\underline{\boxed{\pink{\sf x = -1}}} [/tex]

What are the values of a, b, and c in the quadratic equation –2x2 + 4x – 3 = 0? a = 2, b = 4, c = 3 a = 2, b = 4, c = –3 a = –2, b = 4, c = 3 a = –2, b = 4, c = – 3

Answers

Answer:

Option D is correct answer.

Step-by-step explanation:

Hey, there!

Before finding a,b,c, you remember the formula of quadratic equation,

[tex]a {x}^{2} + bx + c = 0[/tex]

Where, "a" represents thecoefficient of, x^2 "b" represents the coefficient of y and "c" is a numerical value.

So, the value of a,b,c in this equation "-2x^2+4x-3=0" is:

a= -2

b= 4

and c= -3.

Hope it helps...

Answer:

D

Step-by-step explanation:

EDGE 2021

PLAASE HELP ME! I will make BRAINIEST

Answers

Answer:  Answer is the steps.

Step-by-step explanation:

The table of  with   the values  

   

 x           y  

0             3

1              1  

2              -1

3              -3  

It represents a linear function because as the y values decrease by 2  the x values increase by 1.

The number of problems assigned as homework by a savvy math professor is a function of the length of the class on a particular day, which is either 45 minutes, 90 minutes, or 135 minutes. He first multiplies the number of minutes by 4 and then divides that number by 9. Finally, he subtracts 12 from that amount. Which of the following functions best represents the number of math problems the professor assigns depending on the length of the class, t, in minutes?

Answers

Answer:f(t)=4/9t — 12

Step-by-step explanation:

1. 4 is being multiplied by t first then divided by 9 not by 4/9 so there shouldn’t be any parentheses.

2. 12 is being subtracted from this so it should be 4/9t—12.

3. Final answer: f(t)= 4/9t — 12

[tex]\frac{1}{8}[/tex]w = 14

Answers

Answer:

w = 112

Step-by-step explanation:

1/8w = 14

Multiply each side by 8

8*1/8w = 14*8

w = 112

Answer: w = 112

Explanation: If w is being multiplied by a fraction, simply multiply both sides of the equation by the reciprocal of that fraction to get w by itself.

So in this problem, since w is being multiplied by 1/8,

we multiply both sides of the equation by 8/1.

On the left, (8/1) (1/8) cancels out and on the right,

if you multiply 14 by 8/1, you get 112.

So w = 112.

Image is attached below.

Why is 1 + (−5) equal to −4?

Answers

Answer:

Step-by-step explanation:

1 + ( -5)     Adding a negative = subtracting:

= 1 - 5

= -4.

Think of these numbers as 'directed' numbers - the numbers depend on the direction.

If we have a thermometer and the temperature reads 1 degree and the temperature drops, the mercury travels down ( negative direction) by 5 units. . It goes down 1 degree to reach 0 then another 4 degrees to reach -4,

1 - 5 = -4.

Given: g(x) = x - 4 and h(x) = 2x - 8,
What is g(h(10))?
0 212
O V6
O V6-8
276 - 8
need help asap and need step by step!!!

Answers

Plug in 10 for x in h(x) then simplify
h(10)=2(10)-8
h(10)=20-8
h(10)=12

h(10) is 12 so put 12 in for g(x)
g(h(10))=12-4
g(h(10))=8

Here’s everything together
g(h(10))=(2(10)-8)-4
=(20-8)-4
=(12)-4
=8

This is what I’ve always done. I can’t really tell what your answers are so sorry if this isn’t right at all.

Simplify
(4 + 2) = (2-(6-6) X 6)​

Answers

Step-by-step explanation:

( 4+ 2 ) = ( 2 - ( 6-6) * 6 )

8 = 2

6

follow me and Mark as brainlist ❤️

16/5 x 36/12 x 25/18

Answers

Answer

[tex]\frac{16}{5}[/tex]*[tex]\frac{36}{12}[/tex]*[tex]\frac{25}{18}[/tex]=[tex]\frac{4}{1} *\frac{2}{3} *\frac{5}{1}=\frac{40}{3} =13\frac{1}{3}[/tex]

Step-by-step explanation:

PLEASE HELP ME ASAP!! Write the following statement as an inequality: 8 less than a number w is under 35.

Answers

Answer:

8<w<35

Step-by-step explanation:

the w has to be over 8, but less than 35, so 8<w<35 is ur answer.

// have a great day //

(WILL GIVE BRAINLIEST!)

Find the distance d(A,B) between points A and B.
A(1,-6); B(1,6)

Answers

Answer:

12

Step-by-step explanation:

use the distance formula

(1-1)^2 + (6- (-6))^2

0+12^2

take the sqrt of 144

12

Answer:

12

Step-by-step explanation:

→To solve this, you need to use the distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

→Plug in the numbers accordingly:

[tex]d=\sqrt{(1-1)^2+(6+6)^2}[/tex]

[tex]d=\sqrt{(0)^2 + (12)^2}[/tex]

[tex]d=\sqrt{144}[/tex]

→Take the square root of 144:

[tex]d=12[/tex]

Please answer this questions please. Will mark brainliest!!! The one with red circled.

Answers

Answer/Step-by-step explanation:

1.a)(iv). [tex] \frac{1}{6} + (-\frac{7}{8} [/tex]

Positive multiplied by negative = negative

[tex] \frac{1}{6} - \frac{7}{8} [/tex]

[tex]\frac{4 - 21}{24} = \frac{-17}{24} = -\frac{17}{24}[/tex]

2a.) 73.48 +(-37.3)

[tex] Note: + * - = - [/tex]

73.48 - 37.3 = 36.18

3c.) [tex] 3\frac{3}{4} [/tex] ÷ [tex] (-4\frac{2}{7}) [/tex]

Convert to proper fraction

[tex] \frac{15}{4} [/tex] ÷ [tex] (-\frac{30}{7}) [/tex]

Change ÷ to × and flip the fraction on your right upside down

[tex] \frac{15}{4} * (-\frac{7}{30}) [/tex]

[tex] -\frac{15*7}{4*30} [/tex]

[tex] -\frac{1*7}{4*2} = -\frac{7}{8} [/tex]

3d.) -52.25 ÷ (-5.5) = [tex] \frac{-52.25}{-5.5} [/tex]

(Note: - ÷ - = + )

[tex] \frac{-52.25}{-5.5} = 9.5 [/tex]

The yearly attendance at a local restaurant is 48,300 and grows continuously at a rate of 6.8% each year. What is the approximate attendance at the restaurant in 18 years?

Answers

The approximate attendance at the restaurant in 18 years would be 59,119.

If 2+3=5, Then _____ ______.

Answers

Answer:

3+2=5

Step-by-step explanation:

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