Find an exponential function that passes through (2,8) and (4,128)

Answers

Answer 1

The final exponential function using the values of 'a' and 'b':
y = (1/2)(4^x)

To find an exponential function that passes through the points (2,8) and (4,128), follow these steps:

Step 1: Recall the general form of an exponential function: y = ab^x
Here, 'a' and 'b' are constants that need to be determined using the given points.

Step 2: Substitute the first point (2,8) into the equation:
8 = ab^2

Step 3: Substitute the second point (4,128) into the equation:
128 = ab^4

Step 4: Divide the second equation by the first equation to eliminate 'a':
(128 = ab^4) / (8 = ab^2)
16 = b^2

Step 5: Solve for 'b':
b = √16
b = 4

Step 6: Substitute the value of 'b' back into the first equation:
8 = a(4^2)

Step 7: Solve for 'a':
8 = 16a
a = 8/16
a = 1/2

Step 8: Write the final exponential function using the values of 'a' and 'b':
y = (1/2)(4^x)

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Related Questions

find an equation of the circle that satisfies the given (−7, −5); radius 8

Answers

The equation of the circle is (x + 7)^2 + (y + 5)^2 = 64.

The equation of a circle can be written in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r is the radius. Given that the center of the circle is (-7, -5) and the radius is 8, we can substitute these values into the equation: (x - (-7))^2 + (y - (-5))^2 = 8^2. Simplifying the equation, we get: (x + 7)^2 + (y + 5)^2 = 64. Therefore, the equation of the circle is (x + 7)^2 + (y + 5)^2 = 64.

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The portions of gold in three bracelets are shown. Which bracelet has the highest portion of gold? A. 62% B. 3/5 C.0.65

Answers

The portion of gold in three bracelets that are shown. The bracelet that has a portion of gold is 0.65. The correct option is c.

What is gold?

Gold is actually a very soft metal. Rings constructed of pure gold would bend and disfigure over time. Other elements are added to strengthen the ring. 100% gold is far too soft and far from as durable as it should be.

Gold is a pure element. It is found in the earth's crust when making jewellery from gold, and some other metals like copper or silver is mixed with it.

Therefore, the correct option is c. 0.65.

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recursion is sometimes required to solve certain types of problems. true/false

Answers

True. Recursion is often necessary to solve certain types of problems that exhibit a recursive structure or require repeated subproblem solving.

Recursion is a programming technique where a function calls itself in its own definition. It allows for the decomposition of complex problems into smaller, more manageable subproblems that can be solved recursively. Recursion is particularly useful when problems exhibit a recursive structure, such as tree traversal, backtracking, or divide-and-conquer algorithms.

For example, problems like computing the factorial of a number, calculating Fibonacci numbers, or traversing a binary tree can be elegantly and efficiently solved using recursion. These problems can be broken down into smaller instances of the same problem until a base case is reached, and then the solutions are combined to solve the original problem.

However, it's worth noting that not all problems require recursion for their solution. There are alternative approaches, such as iterative loops or dynamic programming, which can be used depending on the problem's characteristics and requirements.

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Construct the Fuli binary tree, whose Post-order traversal: G L B V T AUIE and Prevorder Traversal : E B G L A A T U. (2M) Aso display the In- (1M)

Answers

The in-order traversal of the tree represents the elements in ascending order, starting from the leftmost node to the rightmost node. In the case of the Fuli binary tree, the in-order traversal is **G L B A A I E T U**.

The Fuli binary tree can be constructed using the given post-order and pre-order traversals: Post-order traversal: **G L B V T AUIE**, Pre-order traversal: **E B G L A A T U**.

To construct the tree, we can use the following steps:

1. Identify the root of the tree: In the pre-order traversal, the first element is the root, so in this case, the root is **E**.

2. Locate the root in the post-order traversal: Since post-order traversal visits the left subtree first, we can find the root in the post-order traversal to divide it into left and right subtrees. In this case, we find **E** in the post-order traversal.

Recurse for left and right subtrees: Repeat steps 1-4 for the left and right subtrees using the divided pre-order and post-order traversals.

Using the above steps, we can construct the Fuli binary tree:

```

           E

         /    \

     B G L A A  T U

             \

              I E

```

In-order traversal of the constructed Fuli binary tree: **G L B A A I E T U**.

The in-order traversal of the tree represents the elements in ascending order, starting from the leftmost node to the rightmost node. In the case of the Fuli binary tree, the in-order traversal is **G L B A A I E T U**.

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100 students had some homework
42 of the students were boys
8 of the 100 did not do their homework
53 of the girls did their homework

Answers

Answer:

Here is answer

...........

please give Brainliest

100 students had some homework 42 of the students were boys 8 of the 100 did not do their homework 53

Answer:

is this the homework you have?

Step-by-step explanation:

100 students had some homework 42 of the students were boys 8 of the 100 did not do their homework 53

which graph shows the system x^2+y=2 x^2+y^2=9

Answers

Answer:

The answer is A

Step-by-step explanation:

Answer:

Graph A

Step-by-step explanation:

for edge

Find the value of each variable.

Find the value of each variable.

Answers

The value of angle a is 54⁰.

The value of angle b is 30⁰.

The value of angle c is 96⁰.

What is the value of angle a, b, c?

The value of angle a, b, c is calculated by applying intersecting chord theorem which states that the angle at tangent is half of the arc angle of the two intersecting chords.

m∠a = ¹/₂ x (108⁰) (interior angles of intersecting secants)

m∠a = 54⁰

The value of angle b is calculated as;

m∠b = ¹/₂ x (60⁰) (interior angles of intersecting secants)

m∠b = 30⁰

The value of angle c is calculated as;

adjacent angle to c = ¹/₂ x (108⁰ + 60⁰) (interior angles of intersecting secants)

adjacent angle to c = 84⁰

angle c = 180 - 84⁰ (sum of angles on a straight line)

angle c = 96⁰

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f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6​​​​​​​
where c is constant

Answers

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

where c is a constant.

The solution to the question is shown below.

Step 1: We have given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

We have to find the number of words we have to write to express this function in words.

Step 2: Solution

f(t) = et5+4t + ln(t²+3c)⁷ +te-1+5e⁶

Where,

et5+4t = exponential function

ln(t²+3c)⁷ = natural logarithmic function

te-1 = linear function

e⁶ = exponential function

Therefore, f(t) can be expressed in words as:

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Step 3: Conclusion

Hence, the function f(t) can be expressed in words with:The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

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Which of the following polynomial functions have the same end behavior? Select all that apply.
A. y=-3-x^4
B. y=-2x^2+9x-3
C. y=-3x+5
D. y=x^3-x^2+7x-4

Which of the following polynomial functions have the same end behavior? Select all that apply.A. y=-3-x^4B.

Answers

The answer is b. Y=-2x^2+9x-3

Help me in this question

Help me in this question

Answers

Where is the question

Answer:

1st year: 100-5=95

36000/100 X 95 = 34200

2nd year: 100 + 10 = 110

34200/100 X 110 = 37620

3rd year 100 + 12.5 = 112.5

37620/100 X 112.5 = 42322.50

42322.50 - 36000 = 6322.50

net profit = 6322.50

9/5 - (-6/10)
Khan academy needs either exact fraction or exact decimal

Answers

Answer:

Exact fraction: 6/5

Exact Decimal: 1.2

Answer:

  12/5 = 2.4

Step-by-step explanation:

The fraction 6/10 can be reduced to simplify the addition.

  9/5 -(-6/10) = 9/5 +6/10 = 9/5 +3/5

  = 12/5 = 2.4

__

The two minus signs "cancel." The product of any set of numbers with an even number of minus signs will be positive.

Find the standard form of the equation of the circle with endpoints of a diameter at the points
(4,8) and (2,6).

Answers

(
x

1
)
2
+
(
y

7
)
2
=
37
Explanation:
The center of the circle is the midpoint of the diameter, i.e.
(
7

5
2
,
8
+
6
2
)
=
(
1
,
7
)
Again, the diameter is the distance between the points s
(
7
,
8
)
and
(

5
,
6
)
:

(
7

(

5
)
)
2
+
(
8

6
)
2
=

12
2
+
2
2
=
2

37
so the radius is

37
.
Thus the standard form of the circles equation is
(
x

1
)
2
+
(
y

7
)
2
=
37

Ben has twenty-six coins in her pocket are all dollars(1$ coins) and quarters, and they add up to seventeen dollars in value. How many of each coin does he have

Answers

Answer:

14 $1 coin

12 quarter coin

Step-by-step explanation:

Let :

x = $1 dollar coin

y = $0.25 (1 quarter) coin

x + y = 26 - - - (1)

1x + 0.25y = 17 - - - - (2)

From (1) :

x = 26 - y

Put x = 26 - y in (2)

1(26 - y) + 0.25y = 17

26 - y + 0.25y = 17

-y + 0.25y = 17 - 26

-0.75y = - 9

Divide both sides by - 0.75

-0.75y /- 0.75 = - 9 / - 0.75

y = 12

Put y = 12 in (1)

x = 26 - 12

x = 14

Which function in vertex form is equivalent to f(x)=4+x^2-2x

Answers

Answer:

f(x)=(x-1)²+3

Step-by-step explanation:

f(x)=4+x²-2x=x²-2x+1+3=(x-1)²+3

HELPPP i have 14 left to answer ejvevkjwnd

HELPPP i have 14 left to answer ejvevkjwnd

Answers

Bottom right one is the range

An assembly line has 10 stations with times of 1, 2, 3, 4, …, 10, respectively. What is the bottleneck time?

Answers

The bottleneck time is 10, as this is the longest time for any station in the assembly line.

What is the bottleneck time?In this assembly line, the bottleneck time is 10. This is the amount of time it takes for a product to pass through the longest station, station 10, and is the limiting factor in the line's overall efficiency.This is referred to as the bottleneck time because it is the maximum time that can be achieved, regardless of how efficient the other nine stations are.The bottleneck time is an important concept in assembly line and production management, as it helps to determine the optimal speed of the line and the maximum output that can be achieved.If the bottleneck time is longer than necessary, it can lead to higher costs and slower production.To improve the bottleneck time, managers can look for ways to reduce the time it takes to complete each task, or reduce the number of tasks required.Additionally, managers may need to invest in additional resources, such as robots, to increase the speed of the bottleneck station.

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What are the slope and y-intercept of the line 4y = -x - 32? PLEASE HELP

What are the slope and y-intercept of the line 4y = -x - 32? PLEASE HELP

Answers

Answer: slope -1/4 y intercept -8

Step-by-step explanation:

In the form y = mx+b, m is the slope and b is the y-intercept. So let’s get it into this form, by getting y by itself.

4y = -x - 32

divide by 4 on every term

y = -1/4x - 8

therefore the slope is -1/4 and y intercept is -8

HELP!
Choose all that give the correct expression for the quantity described.
The difference of nine times a number x and the quotient of that number and 5.
9x − x over 5
Eight more than the quotient of twelve and a number n.
n over 12 + 8
The product of a number and the quantity ’six minus the number’ plus the quotient of eight and the number.
x(6 − x) + 8 over x
Sum of three consecutive even integers.2x + (2x + 2) + (2x + 4)

Answers

uhm that’s confusing i have no idea

Answer:

did u ever get on answer cause I'm stuck in this too

Step-by-step explanation:

2. Solve 3^4x-5 = (1/27)^2x+10 for x. Show your work

I know it equals around the negatives but that's it

Answers

It looks like the equation is supposed to read

3⁴ˣ ⁻ ⁵ = (1/27)²ˣ ⁺ ¹⁰

Recall that 3³ = 27, so 1/27 = 3⁻³ :

3⁴ˣ ⁻ ⁵ = (3⁻³)²ˣ ⁺ ¹⁰

Distribute the exponent on the right side:

3⁴ˣ ⁻ ⁵ = 3 ⁻⁶ˣ ⁻ ³⁰

The exponents must be equal for this equation to hold, so

4x - 5 = -6x - 30

Solve for x :

10x = -25

x = -25/10 = -5/2

Write the equation of a line in slope/intercept form given m=0 , and it goes through the point (-2,5).

Answers

Answer:

y=5

Step-by-step explanation:

Use the given slope and point to substitute into the point-slope formula then you can solve for slope/intercept form

Tip: If the slope is 0 the equation is going to be y= the y of your original point (-2,5)

What was the winner's speed during last year's race? (3 points for speed, 2 points for conversion to knots).
Given: 6076 feet/nautical mile.
The winner's time was 16.5 minutes.
(distance unknown)

Part VIII of 2.11.2 Project: Performance Task: The Parrallax Problem apex

Answers

The speed of the winner based on the information is 368.24 mile per minutes

How to calculate the speed ?

It should be noted that speed is calculated as the distance divided by the time given.

The following can be deduced from the information given:.

Distance = 6076 feet/nautical mile.

Time =16.5 minutes.

Speed = Distance / Time

Speed = 6076 / 16.5

Speed = 368.24 mile per minutes

The speed is 368.24 mile per minutes.

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Pls does anyone know what I need to do to move on I've tried plotting another point but it won't let me? Pls if anyone knows tell me asap! I'll give 80 points!

Pls does anyone know what I need to do to move on I've tried plotting another point but it won't let

Answers

A graph of the solution (4, 4) for the system of linear equations is shown in the image attached below.

What is the x-intercept?

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In this context, we would replace the y-value of the first equation 4x - 2y = 8 with zero (0) as follows;

4x - 2(0) = 8

4x = 8

x = 2 ⇒ (2, 0).

For the y-intercept of the first equation 4x - 2y = 8, we would substitute the x-value with zero (0) as follows;

4(0) - 2y = 8

2y = -8

y = -4 ⇒ (0, -4).

For the y-intercept of the first equation y = 3x/2 - 2, we would substitute the x-value with zero (0) as follows;

y = 3(0)/2 - 2

y = -2 ⇒ (0, -2).

Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of linear equations is at the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is equal to the ordered pair (4, 4).

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Pls does anyone know what I need to do to move on I've tried plotting another point but it won't let

find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.
1. 2, (3,9) 2. 5, (1,8)

Answers

Answer:

1. y=2x+3

2. y=5x+3

Step-by-step explanation:

1. to find equation of the line we need the gradient and y-intercept

gradient=2

y=mx+c where m is gradient,x and y are coordinates and c is the y-intercept

input given coordinates and gradient in the equation to find c:

9 = 2(3)+c

9 = 6+c

9-6 = c

c = 3

to write the equation we only input gradient and y-intercept:

y=2x+3

2. to find the equation of the line we need the gradient and y-intercept

gradient=5

y=mx+c where m is gradient,x and y are coordinates and c is the y-intercept

input given coordinates and gradient in the equation to find c:

8 = 5(1)+c

8 = 5+c

8-5 = c

c = 3

to write equation we only input gradient and y intercept:

y=5x+3

please help me out with this one

please help me out with this one

Answers

Answer:

(0.2x -3.2)×5=1.8×5

5

0.2x-3.2=1.8×5

0.2x-3.2=9

0.2x=9+3.2

0.2x=12.2

x=12.2

0.2

x=61

this is your answer.mark me as a brainlist plz.

For a graph of speed in miles per hour as a function of time in hours, what does it mean when the function is increasing? Decreasing?

Answers

When the function is increasing, the speed is increasing and when the function is decreasing, the speed is decreasing

What does it mean when the function is increasing? Decreasing?

The graph is given as:

The graph of speed in miles per hour as a function of time in hours

This can be represented as

S(t)

Where S represents the speed and t represents time

When the function is increasing, the speed is increasing and when the function is decreasing, the speed is decreasing

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i kinda need help on this

i kinda need help on this

Answers

Answer:

16 units²

Step-by-step explanation:

Formula for the area of a parallelogram is given as, A = b*h

Where,

Base (b) = 4

Height (h) = √(5² - 3²) = 4 (Pythagorean theorem)

Plug in the values

Area of parallelogram, A = 4*4

= 16 units²

I need help on this please ​

I need help on this please

Answers

Ya I think it is also the second one

three shrimp boats supply the shrimp wholesalers on hilton head with fresh catch. the annabelle takes 50% of its catch to hudson's, 20% to captain j's, and 30% to mainstreet. the curly q takes 40% of its catch to hudson's, 40% to captain j's, and 20% to mainstreet. the slojoe takes 30% of its catch to hudson's, 40% to captain j's, and 30% to mainstreet. one week hudson's received 242.7 pounds of shrimp, captain j's received 217 pounds, and mainstreet received 159.3 pounds. how many pounds of shrimp did each boat catch?

Answers

Annabelle supplied 121.35 pounds of shrimp, Curly Q supplied 96.9 pounds of shrimp, and Slojoe supplied 72.81 pounds of shrimp.

The three shrimp boats, Annabelle, Curly Q, and Slojoe, collectively supplied 242.7 pounds of shrimp to Hudson's, 217 pounds to Captain J's, and 159.3 pounds to Mainstreet.

Annabelle supplied 50% of its catch to Hudson's, 20% to Captain J's, and 30% to Mainstreet. Therefore, Annabelle supplied: (242.7 x 0.5) = 121.35 pounds of shrimp to Hudson's, (217 x 0.2) = 43.4 pounds of shrimp to Captain J's and (159.3 x 0.3) = 47.79 pounds of shrimp to Mainstreet.

In total, Annabelle supplied = 121.35 + 43.4 + 47.79 = 212.54

Curly Q supplied 40% of its catch to Hudson's, 40% to Captain J's, and 20% to Mainstreet. Therefore, Curly Q supplied (242.7 x 0.4) = 96.9 pounds of shrimp to Hudson's, (217 x 0.4) = 86.8 pounds of shrimp to Captain J's, and               (159.3 x 0.2) = 31.86 pounds of shrimp to Mainstreet.

In total, Curly Q supplied = 96.9 + 86.8 + 31.86 = 215.56

Slojoe supplied 30% of its catch to Hudson's, 40% to Captain J's, and 30% to Mainstreet. Therefore, Slojoe supplied (242.7 x 0.3) = 72.81 pounds of shrimp to Hudson's, (217 x 0.4) = 86.8 pounds of shrimp to Captain J's, and              (159.3 x 0.3) = 47.79 pounds of shrimp to Mainstreet.

In total, Slojoe supplied = 72.81 + 86.8 + 47.79 = 207.4


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Which is the approximate measure of angle yzx? 34.8° 39.4° 50.6° 55.2°

Answers

The measure of <YZX is 55.2 degree.

What is Trigonometry?

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

XY= 12.4 cm, YZ= 15.1 cm

In right ΔXYZ with hypotenuse XZ and opposite side XY to ∠YZX then

Using the sine ratio

sin <YZX= 12.4/ 15.1

sin <YZX = 0.8211

<YZX= 55.2

Hence, the measure of <YZX is 55.2 degree

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Answer: 55.2

Step-by-step explanation: just took it

Which is the approximate measure of angle yzx? 34.8 39.4 50.6 55.2

Profit is the difference between revenue and cost. The revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial 2x3 + 30x – 130. The cost, in dollars, of producing the skateboards can be modeled by 2x3 – 3x – 520. The variable x represents the number of skateboards sold.

What expression represents the profit?

27x – 650
27x + 390
33x – 650
33x + 390

Answers

The expression which represents the profit is 33x + 390, the correct option is D.

What is an expression?

Expression in mathematics is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given that;

The polynomial= 2x3 + 30x – 130

The cost, in dollars, of producing the skateboard= 2x3 – 3x – 520.

Now,

To find the expression that represents the profit, we need to subtract the cost from the revenue. So, we have:

profit = revenue - cost

profit = (2x^3 + 30x - 130) - (2x^3 - 3x - 520)

profit = 2x^3 + 30x - 130 - 2x^3 + 3x + 520

profit = 33x + 390

Therefore, the expression will be 33x + 390.

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