A curve passes through a point P(0, 3) and has the property that slope of curve at every point P is twice the y-coordinate of point P. Use the concept of exponential growth function to find the equation of curve.

Answers

Answer 1

Answer:

The equation of curve is [tex]y = 3\cdot 7.389^{x}[/tex].

Step-by-step explanation:

The exponential growth function is represented by the expression described below:

[tex]y = a\cdot b^{x}[/tex] (1)

Where:

[tex]x[/tex] - Independent variable.

[tex]y[/tex] - Dependent variable.

[tex]a[/tex] - Initial value of [tex]y[/tex].

[tex]b[/tex] - Base.

By deriving (1), we obtain an expression for the slope of the curve:

[tex]y' = a\cdot b^{x} \cdot \ln b[/tex] (2)

If we know that [tex]x = 0[/tex], [tex]y = 3[/tex] and [tex]y' = 6[/tex], then we have the following system of equations:

[tex]a = 3[/tex] (3)

[tex]a\cdot \ln b = 6[/tex] (4)

By (3) in (4):

[tex]3\cdot \ln b = 6[/tex]

[tex]\ln b = 2[/tex]

[tex]b = e^{2}[/tex]

[tex]b = 7.389[/tex]

Therefore, the equation of curve is [tex]y = 3\cdot 7.389^{x}[/tex].


Related Questions

Question 4 Are there any outliers in the data sets? If there are outliers, do they lie at the lower end or at the higher end of the data sets?
(data sets are provided below!)

Walden’s data set: 2, 2, 2, 3, 3, 3, 3, 4, 4, 4
Drake’s data set: 3, 3, 4, 4, 4, 4, 5, 6, 7, 9

*PLS HELP, THIS IS PASS DUE*

Answers

Answer:

The center of Walden’s data, 3, is less than the center of Drake’s data set, 6.

Step-by-step explanation:

Answer:

Walden’s data set doesn’t have any outliers. Drake’s data has an outlier with the value 9, which is at the higher end of the distribution.

Step-by-step explanation:

Hope this helped!

please answer 1-7 I BEG YOU I WILL MARK BRAINLIEST

Answers

Use the Circumference Formula of a Circle: C=2(pi)(r). The radius is the length from the center to a point on the circle. The circumference is essentially the perimeter of the circle, so the “edge” around the circle is the circumference.
1. 28.26
2. 50.24
3. 65.94
4. 131.88
5. 34.54
6. 197.82
I hope this helps!

What value of xwill make x3/2=8 true?

Answers

Answer:

is it x to the power of 3 or 3x over 2=8?

Step-by-step explanation:

Answer:

x = ∛2^4 which is approx. 2.5

Step-by-step explanation:

x³/2 = 8/1

cross-multiply to get:

x³ = 16

x³ = 2^4

multiply each exponent by 2/3

x^(3·2/3) = 2^(4·2/3)

x² = 2^8/3

take square root of each side:

x = 2^(8/3 · 1/2)

x = 2^4/3

x = ∛2^4

if a dress costs $27,000 when it is on sale for 10% off, what is its original cost?

Answers

Answer:

30,000

Step-by-step explanation:

10% of 30,000 is 3,000

30,000 - 3,000 = 27,000

Which of the following measures cannot be determined from a box plot?
select all that apply.
A. Interquartile range
B. Mean
C. Mean absolute deviation
D. Median
E. Mode
F.Range​

Answers

3 Answers:B) MeanC) Mean absolute deviationE) Mode

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

Explanation:

The box plot, aka "box-and-whisker plot", visually represents five things. These things are:

MinimumQ1 = first quartileMedian (sometimes referred to as Q2 or second quartile)Q3 = third quartileMaximum

This list of five items is known as the five number summary.

The min is the tip of the left most whisker, assuming there aren't any small outliers. The max is the opposite side, being the tip of the right most whisker (assuming no large outliers). If there are any outliers, then they'll be shown as "island" dots on their own separated from the main box plot. The left and right edges of the box are Q1 and Q3 respectively. The median is the vertical line inside the box. The vertical line does not have to be at the midpoint of the left and right edges of the box. It simply needs to be somewhere in the box.

--------

Since the box plot lets us know the min and max, we can compute the range because

range = max - min

and we can also calculate the interquartile range (IQR) because

IQR = Q3 - Q1

--------

So to summarize so far, the five number summary is visually represented as the box plot. The range and IQR can be computed using items from the five number summary.

We cannot compute the mean because we would need the actual data set of values, rather than the summary data. The same goes for the mean absolute deviation (MAD) and the mode. Since your teacher is looking for things that cannot be determined from a box plot, we'll go for answers B, C and E.

In other words, we rule out choices A, D, and F because we can compute or determine those values from a box plot.

What is the value of x in the following equation?

7/8x=42

Answers

7/8= 0.875 so divided 42/0.875=48 so
7/8 multiple by 48 = 42 so the value of x is 48

Help immediately due yesterday show how you got the answer and show your work for brainiest must do both

Answers

12. Each section of the line on each side is identical (shown by the marks through each line)

This means both those angles are also the same.

6x + 1 = 9x-23

Add 23 to both sides

6x + 24 = 9x

Subtract 6x from both sides

24 = 3x

Divide both sides by 3

X = 8

13. Both angles when added together need to equal 180

5x-24 + 8x +9 = 180

Combine like terms

13x -15 = 180

Add 15 to both sides

13x = 195

Divide both sides by 13

X = 15

#12

6x+1=9x-233x=24x=8

#13

8x+9+5x-24=18013x-15=18013x=195x=15

Which description explains how uplift can form mountain ranges?
O A. Wind and water carve rock layers and valleys that leaves some rock layers higher over thousands of years.
O B. Lava from underground volcanoes flows through a surface opening in the crust and cools over hundreds of years.
O c Earthquakes cause large blocks of rocks to fall below the ridges of higher surrounding rock layers over tens of years.
Oo. Forces in the crust push toward each other and cause a section of rock to rise above the surrounding rock over millions of years











Answers

Answer: d. Forces in the crust push toward each other and cause a section of rock to rise above the surrounding rock over millions of years

Step-by-step explanation:

Uplift refers to when the earth's crust is forced to rise above the surrounding area due to pressure from underneath (sometimes this pressure can be from above). It is usually the result of forces of compression pulling plates together.

As these plates collide with one another over millions of years, the rock at the collision boundary is forced to rise above the surrounding rock thereby resulting in an uplift.

If the area of a square is 9, then the perimeter of the
square is

Answers

Answer:

12.

Step-by-step explanation:

The side length = sqrt 9 = 3

so the perimeter = 4*3 = 12.

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

12 units.  

»»————- ★ ————-««  

Here’s why:  

The formula for area of a square is:

[tex]A=s^2\\\\\boxed{\text{Key:}}\\\\s-\text{Side length given.}[/tex]

⸻⸻⸻⸻

We are given the area of the square, 9. To find the side length of the square, required to get the perimeter, we would have to take the square root of 9.

Recall that the area of a square is the square of it's side length. [tex](s^2)[/tex]⸻⸻⸻⸻

[tex]\boxed{\text{Finding the side length of the square:}}\\\\\rightarrow S=9\\\\\sqrt{9}=3\\\\\rightarrow S=\boxed{3}^2[/tex]

⸻⸻⸻⸻

The side length of the square is 3 units.

⸻⸻⸻⸻

The formula for perimeter of a square is:

[tex]P=4(s)\\\\\boxed{\text{Key:}}\\\\s-\text{Side Length}[/tex]

⸻⸻⸻⸻

We have previously calculated the side length of the square, which is 3.We would have to multiply 3 by 4 to get the perimeter.

Recall that the perimeter of a square is 4 times the side length. [tex]4(s)[/tex].

⸻⸻⸻⸻

[tex]\boxed{\text{Finding the perimeter of a square:}}\\\\P=4(3)\\\\\boxed{P=12}[/tex]

⸻⸻⸻⸻

The perimeter of the square is 12 units.

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

brainliest help fast plz

Answers

Answer:

[tex]\frac{5}{16}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2}-\frac{3}{16}=\frac{8}{16}-\frac{3}{16}=\boxed{\frac{5}{16}}[/tex]

Answer:

hope this helps

Step-by-step explanation:

the answer is 5/16

What is the solution to the system of equations graphed below? y = -2x - 3 y = 3x + 2 O A. (-1,1) B. (0,2)​

Answers

Answer:

A. (1-,1)

How ?: Just plug in -1 in the x spot and 1 in the y spot on both sides... If answers are the same that’s the answer.

What percent of 36 is 20?

Answers

Answer:

55.56%

Step-by-step explanation:

Answer:

55.56

Step-by-step explanation:


Does anyone mind helping?

Answers

Answer:

its a and c

Step-by-step explanation:

bc im smart hah its a and c

Answer:

Lines A and C are parallel

Step-by-step explanation:

helppppppp meeeeeeeee fastttttttttttt plssssssssss

Answers

It’s both. Both answers are correct.

Hello! The Answer is A and B

Hope this helps, Have a wonderful day!

Tysm for brainly!

Can someone please help me with this! This is due today and I'm having a hard time! Please help me!

Answers

Answer:

a) Daniel has 55

b) Daniel has 105

c) Daniel has 5z

d) 115 divided by 5, which is 23!!!


HELP HELP HELP HELP

What is the equation of the trend line in the scatter plot ?

Answers

Answer:

The equation for the trend line is y=2x-10

2) How many 1/3 liter servings are in 4/5 liter of Gatorade? *

Answers

I think there’s like 2

I really need help with this.

Answers

Answer:

135

Step-by-step explanation:

All the angles that would correspond with the angle measure 8 (135°) would be m<5, m<2, m<1.

hope this helped!

PLZ ANSWER NO LINKS or i will Ban u...

Answers

Answer:

Grape Juice 250

Apple Juice 2,250

Ginger Ale 2,500

What goes where
+ - x and divide simble

4_(3_2)_6_1=14

Answers

Answer:

(left to right) multiply; add; subtract; divide

Step-by-step explanation:

4*(3+2)-6/1

4*(5)-6/1

20-6/1

20-6

14

14. A company uses many different delivery
services. The probability that any given parcel
will be sent by the ABC Speedy Delivery Service
is 0.71. The probability that the parcel will arrive
on time given the ABC Speedy Delivery
Company was used is 0.93. If a parcel is
randomly selected, find the probability that it will
be sent with the ABC Speedy Delivery Company
and arrive on time.

Answers

Answer:

0.6603 = 66.03% probability that it will be sent with the ABC Speedy Delivery Company and arrive on time.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Sent by ABC Speedy Delivery Service.

Event B: Arrived on time.

The probability that any given parcel will be sent by the ABC Speedy Delivery Service is 0.71.

This means that [tex]P(A) = 0.71[/tex]

The probability that the parcel will arrive on time given the ABC Speedy Delivery Company was used is 0.93.

This means that [tex]P(B|A) = 0.93[/tex]

Find the probability that it will be sent with the ABC Speedy Delivery Company and arrive on time.

This is [tex]P(A \cap B)[/tex]. So

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(A \cap B) = P(B|A)*P(A) = 0.93*0.71 = 0.6603[/tex]

0.6603 = 66.03% probability that it will be sent with the ABC Speedy Delivery Company and arrive on time.

HELP PLZZZZZ
Which of the following are not linear functions? Place a check mark in the box next to each equation that is not a linear function.
A. x = 4
B. y = 5
C. y = 3x + 2
D. y = 2x 2 + 1
E. y = x 2

Answers

Answer:

The option E is not linear function

bcz the in option E there is y =x2

Sylvia bought 8 bags of stickers. Each bag costs $2.79 how much did Sylvia spend

Answers

Answer:

Sylvia's total cost=$2.79*8

=$22.32

Step-by-step explanation:

At a coffee shop, the first 100 customers'
orders were as follows.
Small
Medium
Large
Hot
5
48
22
Cold
8
12
5
What is the probability that a customer ordered
a medium given that he or she ordered a hot
drink?
Rounded to the nearest percent, [? ]%

Answers

Answer:

48%

Step-by-step explanation:

48/100 = 48%

Edit: the awnser is 64% because 48/75 = 64%

The probability that a customer ordered a medium given that he or she ordered a hot drink is,

⇒ 48%

What is mean by Probability?

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

At a coffee shop, the first 100 customers orders were as given.

Now,

Total customer = 100

Order hot median coffee = 48

Thus, The probability that a customer ordered a medium given that he or she ordered a hot drink is,

⇒ 48 / 100

⇒ 0.48

⇒ 48%

Thus, The probability that a customer ordered a medium given that he or she ordered a hot drink is,

⇒ 48%

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ7

Fifteen is the quotient of thirty-two and a number

Answers

Off thirty two and fifty three 53

A right triangle has a leg of length 6 and a hypotenuse of length 21 yards. Find the length of the other leg (nearest tenth).​

Answers

Answer:

20.1

Step-by-step explanation:

a^2+b^2=c^2

6^2+b^2=21^2

36+b^2=441

b^2=441-36

b^2=405

sqrt of b =20.12



Answers are 0-5 5-10 10-15 15-20 20-25

Answers

It’s 10 to 15 because yeah cause I know cause I did that

jose has 3 genres of songs on his Mp3 player. Half of the songs are country songs. A fourth of the songs are rock. The other 10 songs are jazz. If his MP3 player is playing songs at random and on repeat, what is the probability that it will play a rock song followed by a country song

Answers

Answer:

because he has the rock next to the country song

3. A palm free is 12m in height.
A coconut tree is 16m in height.
What is the combined height of the
trees?

Answers

Answer:

12+16= 28m

28m is the combined height of the trees .

Hope this helps !

red works at the convenience store for $7.00 an hour. If he makes $49.00 over 2 days, how many hours did Fred work?

Answers

7 hours is the answer.

7 x 7 = 49, so if he works 7 hours for $7 an hour, he would have $49.

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