Find the exponential function of the 2 points (3, 7) and (5, 63). Use
the formula f(x) = a(b)”.

Answers

Answer 1

Answer:

We obtained the two exponential functions:

[tex]y\:=\:\frac{7}{27}\left(3\right)^x[/tex][tex]y\:=-\:\frac{7}{27}\left(-3\right)^x[/tex]

Step-by-step explanation:

As we know that the exponential function is of the form

f(x) = abˣ

Given the points

(3, 7)(5, 63)

We know these points belong to the exponential function.

so substituting the values (3, 7) and (5, 63) in the function

putting (3, 7)

y = abˣ  

7 = ab³

also putting (5, 63)

y = abˣ

63 = ab⁵

Considering the 2nd equation

63 = ab⁵

as

[tex]a^b\times \:a^c=a^{b+c}[/tex]

so

63 = ab³×b²  

substituting 7 = ab³ in 63 = ab³×b²  

63 = 7 × b²

b² = 63/7

b² = 9

b = ± 3

If b = 3

plug in b = 3 in the equation 7 = ab³ to find the value 'a'

7 = ab³

7 = a(3)³

7 = a × 27

a = 7/27

so, a = 7/27 and b = 3 would give us the function

y = abˣ

[tex]y\:=\:\frac{7}{27}\left(3\right)^x[/tex]

if b = -3

plug in b = -3 in the equation 7 = ab³ to find the value 'a'

[tex]\:7\:=\:a\left(-3\right)^3[/tex]

[tex]a\left(-27\right)=7[/tex]

[tex]a=-\frac{7}{27}[/tex]

so, a = -7/27 and b = -3 would give us the function

y = abˣ

[tex]y\:=-\:\frac{7}{27}\left(-3\right)^x[/tex]

Thus, we obtained the two exponential functions:

[tex]y\:=\:\frac{7}{27}\left(3\right)^x[/tex][tex]y\:=-\:\frac{7}{27}\left(-3\right)^x[/tex]


Related Questions

Plot -7 in the complex plane.

Answers

Answer:

the phone with me and I will be in the future of our games in call of duty Black ops game clip is not available for remote playback of the phone with me know if I can be used for

Step-by-step explanation:

explain the IF

poem in 5 linesexplain the IF

poem in 5 lines

explain the IF

poem in 5 linesexplain the IF

poem in 5 linesexplain the IF

poem in 5 linesexplain the IF

poem in 5 linesexplain the IF

poem in 5 linesexplain the IF

poem in 5 linesexplain the IF

poem in 5 linesexplain the IF

poem in 5 linesexplain the IF

poem in 5 linesexplain the IF

poem in 5 linesexplain the IF

poem in 5 linesexplain the IF

poem in 5 linesexplain the IF

poem in 5 linesexplain the IF

poem in 5 linesexplain the IF

poem in 5 lines

What ordered pair corresponds to point D?
(in pic)
( , ) ?
i’ll give brainiest, don’t answer if you don’t know i need this due in less than 20 mins !!

Answers

Answer:

(2,0)

Step-by-step explanation:

point D is on point (2,0)

that is what it means

Best answer gets Brainliest!!!!

Answers

Answer:

no

Step-by-step explanation:

if it was the amount of time would be going up at a constant rate but its not

and your graph is wrong

hope this helps <3

sorry if this is wrong this is a weird question :/

What is the volume of the following rectangular prism?
units
NI
1
16- units
4.

Answers

Answer:

60

Step-by-step explanation:

The volume of the rectangular prism is V = 64 units³

What is the volume of a prism?

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

The volume of a prism is the product of its base area and height

Volume of Prism = B x h

where B = base area of prism

h = height of prism

Given data ,

Let the volume of the rectangular prism be represented as V

Now , the height of the prism is H = 4 units

The length and width of the prism is 1 and 16 units respectively

So , the base area of the prism B = 16 units²

Now , Volume of Prism = B x h

On simplifying , we get

The volume of rectangular prism V = 16 x 4

The volume of rectangular prism V = 64 units³

Hence , the volume of the rectangular prism is 64 units³

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Twice a number is 42 less than five times a number. What is the number?

Answers

Answer:

21

Step-by-step explanation:

I am 90% sure but tell me if i'm wrong

Sara and Harry are putting together a puzzle. Sara put together 7/12 of the puzzle pieces. Harry put together 7/24 of the puzzle pieces. What fraction of the total number of puzzle pieces has NOT been used? Enter your answer as a fraction, in simplest form, in the box provided.

Answers

Answer:

1/8

Step-by-step explanation:

7/12= 14/24                                    14/24 + 7/24= 21/24                    

21/24= 7/8           1-7/8= 1/8

The fraction of the total number of puzzle pieces has not been used is 1/8.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Sara and Harry are putting together a puzzle. Sara put together 7/12 of the puzzle pieces. Harry put together 7/24 of the puzzle pieces.

The fraction of the total number of puzzle pieces has not been used is calculated as,

7/12= 14/24      

21/24= 7/8        

1-7/8= 1/8

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what is tax dependent​

Answers

Answer:

A dependent is a person other than the taxpayer or spouse who entitles the taxpayer to claim a dependency exemption. Each dependency exemption decreases income subject to tax by the exemption amount.

Step-by-step explanation:

I need help with this !

Answers

The third one because they equal 90

Answer:

the one closer to the right with the 56 and 34

try adding the angle's degree.

Step-by-step explanation:

pleaseee helppp meeee

helppp meee​

Answers

Answer:   Slope = -1.000/2.000 = -0.500

 x-intercept = 0/1 = 0.00000

 y-intercept = 0/2 = 0.00000

Step-by-step explanation:

EASY MATH PLS HELP
For f(x)= 19-5x, what is the value of f(-3)?

Answers

Answer:

f(x)= 19-5(-3)

19+15

f(x)=34

Step-by-step explanation:

What is the relationship between the length of one leg and the length of the hypotenuse of an isosceles right triangles?
A) Leg = Hypotenuse ∙ √2
B) Hypotenuse = Leg ∙ √2
C) Leg ∙ Hypotenuse = √2

Answers

Answer:

B) Hypotenuse = Leg ∙ √2

Step-by-step explanation:

This is a well-known ratio in the 45-45-90 right triangle, but we can derive it.

An isosceles right triangle has two congruent legs forming the right angle and the hypotenuse opposite the right angle. The Pythagorean theorem works since it is a right angle.

Normally, the legs are a and b, and the hypotenuse is c, and we have

a^2 + b^2 = c^2

Here the legs are congruent, so we have a = b.

Substituting a for b, we have

a^2 + a^2 = c^2

2a^2 = c^2

c^2 = 2a^2

c = a√2

Answer: B) Hypotenuse = Leg ∙ √2

Answer:

progably B) Hypotenuse = Leg ∙ √2

Step-by-step explanation:

A club offers me membership for a fee of 20$ plus a monthly fee of 18 b club offers a fee of 14$ and a monthly fee of 20 after how many month will it be the same

Answers

Answer:

wfcfzgcfxfdsdfgfd

Step-by-step explanation:

gfgboy

From A to Z BU
9 Love From A to Z
9 Love From A to Z
20
The
equation d = n²-12n + 43
models the number of defective
items d
produced in a manufacturing process where there
workers in a restricted
are n
area
a) solve for
When
do 30
I
b) solve for n
when
d=20

Answers

Answer:

a) we get value of n: n=10.7 or n=1.2 when d=30

b) we get value of n: n=9.6 or n=2.3 when d=20

Step-by-step explanation:

a) solve for  n When  do= 30

Put d= 30 in the given equation:

[tex]d = n^2-12n + 43[/tex]

[tex]30=n^2-12n+43\\n^2-12n+43-30=0\\n^2-12n+13=0\\[/tex]

Now, we will find value of n by using quadratic formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a=1, b=-12 and c=13

[tex]n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\n=\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(13)}}{2(1)}\\n=\frac{12\pm\sqrt{144-52}}{2}\\n=\frac{12\pm\sqrt{92}}{2}\\n=\frac{12\pm9.59}{2}\\n=\frac{12+9.59}{2} , n=\frac{12-9.59}{2}\\n=10.7 , n=1.2\\[/tex]

So, we get value of n: n=10.7 or n=1.2

b) solve for n  when  d=20

[tex]d=n^2-12n+43\\20=n^2-12n+43\\n^2-12n+43-20=0\\n^2-12n+23=0\\[/tex]

Now, we will find value of n by using quadratic formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a=1, b=-12 and c=23

[tex]n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\n=\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(23)}}{2(1)}\\n=\frac{12\pm\sqrt{144-92}}{2}\\n=\frac{12\pm\sqrt{52}}{2}\\n=\frac{12\pm7.21}{2}\\n=\frac{12+7.21}{2} , n=\frac{12-7.21}{2}\\n=9.6 , n=2.3\\[/tex]

So, we get value of n: n=9.6 or n=2.3

The radius of a cylindrical tank is 3' and the height is 8'what is the volume

Answers

Answer:

226 cubed foot (rounded to 3 s.f.)

Step-by-step explanation:

Volume of cyclinder: [tex]\pi[/tex] × r² × h

Volume of cylindrical tank = [tex]\pi[/tex] × 3² × 8

                                           = 72[tex]\pi[/tex]

                                           = 226 cubed foot (rounded to 3 s.f.)

Plzzzz help!

What is the equation of the line that passes through the point (2,-6) and has a
slope of -12

Answers

Y=-12x+18
Hope this helps :)

write an equatiob of line in slope intercept from passing through (-10,-8) and parallel to y=1/5x-3

Answers

Parallel = same slope
Y = 1/5x + b
Plug in point
-8 = 1/5(-10) + b
-8 = -2 + b, b = -6
Equation: y = 1/5x - 6

Helpppppppppppppppppppppppppppppp

Answers

Answer:

Step-by-step explanation:

c and e is not polynomials

please help. i have like a bunch of missing assignments

Answers

Answer:

The answer is 11 Units

Answer:

12

Step-by-step explanation:

base*height=6*2

6*2=12

The length of a rectangular piece of cardboard is 2 cm greater than its width. If the length and the width were each decreased by 1 cm, the area of the cardboard would be decreased by 27 cm². What are the dimensions of the original piece of cardboard?

Write and solve an equation to represent the problem.

Answers

9514 1404 393

Answer:

  13 cm wide;  15 cm long

Step-by-step explanation:

Let w represent the original width. Then the original length is (w+2) and the original area is w(w+2). After the decrease, the width is (w-1) and the length is (w+1). The decreased area is (w-1)(w+1). The difference between these areas is 27, so we have ...

  w(w+2) -(w-1)(w+1) = 27

 w^2 +2w -(w^2 -1) = 27

 2w +1 = 27

  w = (27-1)/2 = 13

The original piece of cardboard was 13 cm wide and 15 cm long.

If the toss of a coin comes down heads, you win two dollars. If it comes down tails, you lose fifty cents. How much would you expect to gain after 25 tosses (in $ dollars)

Answers

Answer:

$30.00

Step-by-step explanation:

Because if you think about it, about half of them are going to be heads and the other half are going to be tails.

hope this helped

We could expect $30.00 to gain after 25 tosses.

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

It is given that If the toss of a coin comes down heads, you win two dollars. If it comes down tails, you lose fifty cents.

We need to find How much would you expect to gain after 25 tosses (in $ dollars).

Because if you think about it, you will see that about half of them are going to be heads and the other half are going to be tails.

Therefore, We could expect $30.00 to gain after 25 tosses.

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Which set of numbers represents the DOMAIN for the following table below?
X -3 4 6 -12
Y 5 -6 2 0

A
{4,5,6,12}

B
{−12,−3,4,6}

C
{−12,3,4,6}

D
{0,5,−6,2}

Answers

Answer:

B. (-12,-3,4,6)

Step-by-step explanation:

The above question is asking the domain

Write the equation 8x - 5y = 20 in
slope intercept form.

Answers

Answer:

The equation in slope-intercept form is y = 8/5x-4.

I hope this helps! Have a nice day!!

Four ninths plus one ninth

Answers

Answer:

5/9

Step-by-step explanation:

Answer:

5/9

Step-by-step explanation:

4/9 + 1/9

To add fractions, you need a common denominator. You already have a common denominator of 9, so just add the numerators.

4/9 + 1/9 = 5/9

Since there is no common factor of 5 and 9 other than 1, the fraction is already reduced.

Answer: 5/9

Which set of angle measures cannot be the angle measures for a triangle?

Answers

Answer: 60 , 60 , 61

Step-by-step explanation:

be The distance an object travels is determined by how fast it goes and for how long it moves. If an object's speed remains constant, the formula is d= r., where d is the distance, ris the speed, and t is the time. a. If you drive at 50 miles per hour for 5 hours, how far will you have traveled? 200 miles b. 10 miles 250 miles d. 300 miles C. Please select the best answer ​

Answers

Answer:

10 miles is answer because u should divide d=r

I also need help with this question I’m confused

Answers

Answer:

x = 4

Step-by-step explanation:

From the diagram, we can se that line l is parallel to m. This means that according to geometry, m<7 and m<9 are located on the same position on line n. Hence m<7 = m<9 (corresponding angle)

Given

m<7 = 9x+ 5

m<9 = x+37

Equaling both

9x + 5 = x+ 37

9x - x = 37-5

8x = 32

x = 32/8

x = 4

Hence the value of x is 4

Does this set of ordered pairs represent a function? (-1,5)(0,-3)(2,7)(4,0)(7,5)

Answers

Answer:

No

Step-by-step explanation:

You cant have 2 y values

Answer:

it is indeed a function

Step-by-step explanation:

Anthony is 154 cm tall, his brother Gerry is 5/7 as tall as him. How tall is Gerry?

:D can someone please help me with these problems please

Answers

The correct answer is 110 cm

Explanation:

Fractions always include two values (one at the top and the other at the bottom) and they represent the proportion of something, for example, 1/2 of an apple means there is only half apple. Now, to calculate how much is 5/7 of 154 centimeters, simply divide the total number into the denominator (bottom number) and then multiply the result by the numerator (top number). This process is shown in detail below:

[tex]\frac{5}{7}[/tex]  -  5 is the numerator and 7 is the denominator

5/7 of 154 cm

154 cm / 7 = 22

22 x 5 = 110 cm

Which is an equation for the line that contains (-2,5) and has a slope of -7 ?
7x + y = 33
y=-7x+9
y=-7x-33
7y+y=-9

Answers

Answer:

y = -7x - 9

Step-by-step explanation:

The standard from of equation of a line is expressed as;

y = mx+c

m is teh slope = -7

c is the intercept

Get the intercept by substituting m = -7 and the point (-2, 5) into the equation;

y = mx+c

5 = -7(-2) + c

5 = 14 + c

c = 5-14

c = -9

Substitute m = -7 and c = -9 into the expression y = mx+c

y = -7x - 9

Hence the required equation of the line is y = -7x - 9

find the number of permutations of the letters in twelve

Answers

Answer:

360

Step-by-step explanation:

Six letters in twelve with a repeated e would be 6! ÷ 2

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