Model the pair of situations with exponential functions f and g. Find the approximate value of x that makes f(x)= g(x).

f:initial value of 300 decreasing at a rate of 13%
g: initial value of 100 increasing at a rate of 13%

Write the exponential function for f.

f(x)=__

Answers

Answer 1

The solution to the exponential functions are

a) The function f ( x ) = 300 ( 0.87 )ˣ

b) The function g ( x ) = 100 ( 1.13 )ˣ

c) The value of x = 6

What is exponential growth factor?

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the function be represented as f ( x ) and g ( x )

So , the function f ( x ) is decreasing at a rate of 13 %

Substituting the values in the equation , we get

f ( x ) = 300 ( 1 - 0.13 )ˣ

On simplifying the equation , we get

f ( x ) = 300 ( 0.87 )ˣ

And , the function g ( x ) is increasing at a rate of 13 %

Substituting the values in the equation , we get

g ( x ) = 100 ( 1 + 0.13 )ˣ

On simplifying the equation , we get

g ( x ) = 100 ( 1.13 )ˣ

And , the approximate value when f ( x ) = g ( x ) is

300 ( 0.87 )ˣ = 100 ( 1.13 )ˣ

On further simplification , we get

3 ( 0.87 )ˣ = ( 1.13 )ˣ

Taking logarithm on both sides of the equation , we get

ln ( 5 ) + x ln ( 0.87 ) = x ln ( 1.13 )

And , x [ ln ( 1.13 ) - ln ( 0.87 ) ] = ln ( 5 )

On further simplification , we get

x = ln ( 5 ) / [ ln ( 1.13 ) - ln ( 0.87 ) ]

x = 6.15

x = 6

Hence , the exponential equations are solved

To learn more about exponential growth factor click :

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Related Questions

Write ANY FOUR factors of -23 ab2.​

Answers

Answer:

The factors are;

23, -23 , a , b

Step-by-step explanation:

Here, we want to write the factors of the given expression

-23 ab^2

The factors are simply those values or expression that can be divided by the given expressions

We have the factors as follows;

23

-23

a

b

PLEASE HELP ME!!! Ms. Jones wants to install a stone border along the flower bed in her rectangular backyard. Which is closest to the value of F?

A: 16 ft
B: 25 ft
C: 30 ft
D: 53 ft

Answers

Answer:

use Pythagoras theorem formula   [tex]C^{2}[/tex] = [tex]A^{2}[/tex] + [tex]B^{2}[/tex]

Step-by-step explanation:

[tex]C^{2}[/tex] =  [tex]24^{2}[/tex] + [tex]18^{2}[/tex]

[tex]C^{2}[/tex]  = 576 + 324

[tex]C^{2}[/tex] = 900

C = [tex]\sqrt{900}[/tex]

C = 30

Does that make sense?  :|

What is the equation of the line that passes through the point (-7,-4) and has an undefined slope?

Answers

Answer:

When the slope is UNDEFINED, that means the denominator of the slope formula is ZERO .

Slope formula = (y2 - y1)/(x2 - x1), and the graph is a VERTICAL line and the equation of the line is x =7 . Point (7, -4) is a point on the line.

Hope this helps...

Answer:

(-7, anything but 4)

Step-by-step explanation:

Since then you would have something like this

-4+5=1

-7+7=0

8(34a)−8 ummmmm does anyone know

Answers

Answer:

8(34a−1)

Step-by-step explanation:

PLZZ HELPP ILL GIVE BRAINLIST

What is the first step in solving the following equation?
d
-3
6

Answers

Answer:

Multiply by 6 to both sides of the equal sign.

(Please tell me if I am wrong)

Answer:

3.

Step-by-step explanation:

multiply 6 on both sides of equal sign

Given the graph below what is the domain of the exponential function?

a. x>3
b. y>0
c. x>0
d. all real numbers

Answers

Answer:

Domain- All possible x values.

In this case,  the graph goes from -infinity to 3.

So, the answer is x < 3, x is less than 3.

Let me know if this helps!

Hi there! Your answer is all real numbers.

Please see an explanation for a clear understanding to your problem.

Any questions about my answer and explanation can be asked through comments! :)

Step-by-step explanation:

[tex] \large \boxed{ \sf{domain = set \: \: of \: \: all \: \: x - values}}[/tex]

Remember, domain is set of all x-values. Therefore, we can cancel b choice because y>0 is range, not domain.

Given the exponential function

[tex] \large{y = {a}^{x} } \: \: \large({x \in \R}) \: \: \large({y \in \R^{ + } })[/tex]

This is the define of Exponential Function where x is all real numbers and y is all real positive number.

Hence, the define of exponential function proves that x must be all set of real numbers.

How do I find the center and angle of rotation

Answers

9514 1404 393

Answer:

B → XC → YD → Z180° rotation about the origin

Step-by-step explanation:

In general, if PQ is rotated to P'Q', the center of rotation (O) will be the point of intersection of the perpendicular bisectors of PP' and QQ'. The angle of rotation will be the angle POP', or QOQ'.

__

The correspondence between preimage vertices ABCD and image vertices can be found by naming the vertices in the same order (clockwise) from one whose correspondence you know.

Here, the correspondence between A and W is given. Vertices clockwise from W are WXYZ, so those are the image points corresponding to ABCD.

__

We note that the midpoints of AW and BX are coincident at the origin. That is, the perpendicular bisectors of these segments are coincident at the origin, so the origin (point O) is the center of rotation. The rotation angle is AOW, an angle that measures 180°.

__

The image point coordinates are the opposites of the preimage point coordinates.

  A(2, 2) ⇒ W(-2, -2)

  B(2, 5) ⇒ X(-2, -5)

  C(5, 5) ⇒ Y(-5, -5)

  D(5, 2) ⇒ Z(-5, -2)

This is another indication that the rotation is 180° about the origin, since that rotation results in the mapping ...

  (x, y) ⇒ (-x, -y) . . . . . rotation 180° about the origin

PLEASE HELP QUICKLY!!! i have no idea what i’m doing

Answers

Answer:54 degrees

Step-by-step explanation:

If u want to find non you subtract the degrees you already have so it's would be 80-34=54

At the local video rental store,
José rents two movies and threegames for a total of $14.50. At the same time, Meg rents three movies and one game for a total of $9.50. How much money is needed to rent a combination of one game and one movie?

Answers

4 dollars and seventy six cents will be the total

Which function should be used to when evaluating the function at x = 10?

Answers

Answer: p(x)= 2x+10

Step-by-step explanation:

x>4 and x=10 ten is greater than four

Cody's school is selling tickets to the annual talent show. On the first day of ticket sales the school sold 7 senior citizen tickets and student tickets for a total of 196 The school took in $104 on the second day by selling 5 senior citizen tickets and 6 student tickets What is the price each of one senior citizen ticket and one student ticket?

Answers

Complete question:

Cody's school is selling tickets to the annual talent show. On the first day of ticket sales the school sold 7 senior citizen tickets and 14 student tickets for a total of 196 The school took in $104 on the second day by selling 5 senior citizen tickets and 6 student tickets What is the price each of one senior citizen ticket and one student ticket?

Answer :

Señior tickets = $10

Student ticket = $9

Step-by-step explanation:

Let :

Senior ticket = x

Student ticket = y

7x + 14y = 196 - - - (1)

5x + 6y = 104 - - - (2)

Multiply (1) by 5 and (2) by 7

35x + 70y = 980 - - - (3)

35x + 42y = 728 - - - (4)

Subtract (3) and (4)

28y = 252

y = 252 / 28

y = 9

From (1)

7x + 14(9) = 196

7x + 126 = 196

7x = 70

x = 10

Hence,

Señior tickets = $10

Student ticket = $9

Can someone help me with this. Will Mark brainliest. Need answer and explanation/work. Thanks.

Answers

Answer:

Step-by-step explanation:

Please mark brainly if you like my answer

A triangular prism has a base area of 6 centimeters squared and the volume is 36 centimeters cubed. Find the height.

Answers

The height of the equation is 7

What is the relative minimum of the function?



Enter your answer in the box.

Answers

Answer:

Step-by-step explanation:

they want to know the lowest point of the line that is graphed,  do you see that it's  -2 ?

the relative minimum is also the absolute minimum for this questions

For what value of x is the given parallelogram rhombus? I’ll mark the BRAINIEST

Answers

2x + 49 = 8x - 5
54 = 6x
X = 9

what is the volume of this figure?

Answers

Answer:

1125

Step-by-step explanation:

Answer: 875

Step-by-step explanation:

5*15*5 = 375

15*5*5 = 375

5*5*5 = 125

375 +375 + 125 = 875

Evaluate the expression given below for x=5

3(4x-9) = ___________

Answers

Answer:

33

Step-by-step explanation:

3(4x-9)

Plug in 5 as x

= 3(4(5)-9)

= 3(20-9)

= 3(11)

= 33

I hope this helps!

Answer:

33

Step-by-step explanation:

3 x ( 4 x 5 -9 )

3 x (20 -9 )

3 x 11

33

Is the point (4,-3) a solution for this system?

Answers

Yes it is.

Step by step explanation:

HEY CAN ANYONE PLS ANSWER DIS MATH PROBLEM!

Answers

The answer C ! Have a good day

Answer:

I think its C. The dates are 4.75 and the pomegranates are 3.5 which would also be 3.5p and 4.75d so 4.75d+ 3.5p=18

64,000 attended the last NFL football game. 80% of the supporters in attendance were rooting for the home team, and 20% of the supporters in attendance were rooting for the away team. How many people were at the game to support the home team?

Answers

Answer:

12800 People was supporting the home team!

64,000 - 80% = 12800

A kite is stuck in a tree and Joe is holding the string. The angle formed
between the kite string and the tree is 50°. The distance between Joe
and the tree is 12 feet. How long is the kite string? Round to the nearest
tenth.

Answers

Answer:

15 feet

Step-by-step explanation:

Answer:

u04- (Saresp–2008) Nas Lojas Compre Aqui, um micro-ondas pode ser vendido de duas formas: à vista por R$ 299,00 ou em 12 parcelas iguais de R$ 32,15. As amigas Giovana e Mariana compraram, cada uma, um micro-ondas nessa loja: a primeira, à vista e a segunda, a prazo. Assinale a alternativa que mostra a quantia que Mariana pagou a mais do que Giovana.

2 pontos

a) R$ 22,50.

b) R$ 86,80.

c) R$ 129,30.

d) R$ 266,85.

e) Não houve diferença

what's one thing that could possibly end the whole entire world? (p.s.my most recent artwork)​

Answers

climate change, also very nice drawing :)

Answer:

i love ur art its amazeballs and an asteroid thing

Step-by-step explanation:

A rectangle is dilated by a scale factor of y to create a new rectangle. The area of the new rectangle is y2 times the area of the original rectangle.

True or false ?
Please help

Answers

Answer: True

Step-by-step explanation:

Suppose the length and width of the original rectangle is L and W

After dilation by a factor of y, it becomes yL and yW

Area of the original rectangle [tex]A_1=L\times W[/tex]

The area of the dilated rectangle is [tex]A_2=yL\times yW=y^2LW[/tex]

we can see that

[tex]\Rightarrow A_2=y^2A_1[/tex]

Find the area of the trapezoid below

Answers

The total are is 828 cm

#8 PLEASEEEENENDBBXNFJDNNFNBCBCC

Answers

Answer:

a) 45° b) 90°

Step-by-step explanation:

squares have 90 degree angles and half of that is 45

Zachary bought 8.25 pounds of red, white, and blue candies for his Fourth of July party. If 2.5 pounds of the candies are red, and 3.75 pounds are blue, how many pounds of candy are white? Show your work.

Answers

Answer:

2 pounds

Step-by-step explanation:

pounds of white candy: 8.25 - (2.5 + 3.75) = 8.25 - 6.25 = 2

The weight of the white candy in pounds will be 2 lb.

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 Zachary bought 8.25 pounds of red, white, and blue candies for his Fourth of July party. If 2.5 pounds of the candies are red, and 3.75 pounds are blue.

The weight of the white candy will be calculated as,

Pounds of white candy = 8.25 - (2.5 + 3.75)

Pounds of white candy = 8.25 - 6.25

Pounds of white candy = 2 lb

To know more about an expression follow

https://brainly.com/question/29250551

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Given that a/b =2/5 and b/c = 3/4 find a:b:c

Answers

A=6 B=15 C=20 could I get a crown?

Is 3/4y=9 true or false

Answers

<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3

Answer:

Let's solve your equation step-by-step.

3 / 4 y = 9

Step 1: Multiply both sides by 4/3.

(4 / 3 ) * ( 3 / 4 y ) = ( 4 / 3 ) * ( 9 )

y = 12

Answer:

y = 12

<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3

Insert 12 to the y value:

3 / 4 ( 12 ) = 9

9 = 9

True

<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3

Answer:

Yes, True

3/4y = 9

y = 12

Step-by-step explanation:

1. Multiply both sides by the fractions reciprocal

3/4y *4/3 = 9 *4/3

2. Simplify

2a. Cancel terms that are in both the numerator and denominator

y =12

Explain in words how you would graph the point (2,6) on a coordinate plane. please help me

Answers

Answer:

Starting from the origin, move 2 units to the right on the x-axis. Then, move up 6 units on the y-axis.

Answer:

You would find the positive 2 on the horizontal line, then find the 6 of the vertical line. Then you would draw a vertical line on 2 and a horizontal on 6. Find where those two lines intersect and draw a point there.

In the number 73.6592104, which digit is in the thousandths place?

Answers

Answer:

In the number 73.6592104,  the 9 is in the thousandths place.

Let me know if this helps!

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