if a​ true-false test with questions is​ given, what is the probability of scoring ​(a) exactly​ 80% just by​ guessing?

Answers

Answer 1

The probability of scoring exactly​ 80%  is  0.04395  as per the given data.

Given: 10 true-false questions

So, we will have 50% chances (probability = 0.5) of being correct.

P( 80% score) = P( 8 answers correct)

As we observe, if X= number of correct answers, then X~ Binomial (n=10, p=0.5)

So, P(  80% score) = P( 8 answers correct)

= 0.0439453125

= 0.04395

Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.

Probability basically refers to the degree to which something is likely to occur. With the help of this fundamental theory of probability, which is also used to describe the probability distribution, you will discover the possible results for a random experiment. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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Related Questions

Calculate the cfse for a d^3 system in an octahedral field in units of ∆_o. In other words, do not enter "∆_o" with your answer. For example, if your answer is −0. 8∆_o, then enter "−0. 8. "

Answers

The magnetic moment of an octahedral complex with CFSE=0.8Δo and weak field ligands can take the form of Q.

The Crystal Field Stabilization Energy for a (d3 metal in both forms must be determined in order to provide an answer. The chosen geometry will be the one with the greatest stabilization. The Crystal Field Stabilization Energy is therefore CFSE = -0.8 x 4/9 Δo = -0.355 Δo for tetrahedral d3.

The octahedral d7 complex [Co(CN)64-] is also CN—a strong field ligand. Because of its (t2g)6(eg)1 orbital occupancy, it possesses one unpaired electron. The CFSE in this instance is −(6)(25)ΔO+(1)(35)ΔO+P=−95ΔO+P.

The [Ti(H2O)6]3+ complex's crystal field stabilization energy (CFSE), measured in kJ/mol. The first absorption maximum for the transition, according to CFT, is at 20,3000 cm-1.

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Akira is running around a circular track. Akira runs counterclockwise. From where he starts, it takes him 22 seconds to reach the easternmost point of the track. It takes him 95 seconds to run one complete lap. Bob starts running at the same time as Akira. Bob starts from the northernmost point and runs clockwise. Bob and Akira pass each other for the first time after 26 seconds. How long does Bob take to run one lap of the track? (round off your answer to four decimal digits)

Answers

It takes Bob 125.0633 seconds to cover the entire track.

Let the time taken by Bob to cover the track be x sec

Let the distance of the track be y m

Akira covers the whole track in 95 seconds

hence, his speed is y/95 m/s

Similarly, Bob's speed is y/x m/s

He has traveled to the Easternmost point in 22 seconds. Hence to meet Akira, he has to run for 4 more seconds.

In that time he will cover a distance of 4y/95 m

Similarly, in 26 seconds, Bob will cover

26 y/x m/s

Now Akira has started from the Northernmost point, and we all know that the distance between the Easternmost and Northernmost points of the track will be 1/4th of the whole track length.

Hence,

4y/95 + 26y/x = y/4

or, y(4/95 + 26/x) = y/4

or, 4/95 + 26/x = 1/4

or, (4x + 2470)/95x = 1/4

or, 4x + 2470 = 95x/4

or, 16x + 9880 = 95x

or, 79x = 9880

or, x = 125.0633 seconds

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6y-5=7

what is y hdhfhdjshbdhdj

Answers

Answer: Y=2

Step-by-step explanation:

find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius cm. what is the maximum​ volume?

Answers

The dimensions of a right circular cylinder of maximum volume are

[tex]5\sqrt{6}[/tex] and [tex]10\sqrt{3}[/tex].

Given the radius of sphere is 15 cm.

Let's assume radius of right circular cylinder = r

height of right circular cylinder = h.

Since the cylinder is inscribed in the sphere, their centers will coincide. As a result, the height is divided into two equal portions from the sphere's center. Therefore, we can apply Pythagoras' Theorem to get the cylinder's half-height in terms of radius.

[tex]R^2 = r^2 + (h/2)^2.[/tex]

[tex]r^2 = R^2 - h^2/4.[/tex]

Volume of cylinder = [tex]\pi*r^2*h.[/tex]

Now we can substitute value of [tex]r^2[/tex] in volume of cylinder.

V =  [tex]\pi*( R^2 - h^2/4)*h[/tex]

taking  R = 15 .

V = [tex]\pi*(225 - h^2/4)*h[/tex]

V = [tex]\pi*225*h - \pi*h^3/4[/tex]

For maximum volume we have to do derivative of volume  = 0

derivative with respect to h.

V' = [tex]\pi*225 - 3*\pi*h^2/4[/tex]

V' = 0

[tex]\pi*225 - 3*\pi*h^2/4[/tex]= 0

[tex]3*h^2/4 = 225[/tex]

[tex]h^2 = 75*4.[/tex]

h = 10[tex]\sqrt{3}[/tex]

put the value of h in [tex]r^2 = 225 - h^2/4[/tex]

[tex]r^2[/tex] = 225 - (300/4)

[tex]r^2[/tex] = 150

r = [tex]\sqrt{150}[/tex]

r = 5[tex]\sqrt{6}[/tex].

So the dimensions of a right circular cylinder are 10[tex]\sqrt{3}[/tex] and 5[tex]\sqrt{6}[/tex].

Given Question is incomplete, Complete Question here:

find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 15 cm. what is the maximum​ volume?

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8(t+2) -3(t-4=6(t-7)+8

Answers

Answer: T-62

Step-by-step explanation: i think this is correct

The solution is, the value we get, t = 62.

What is  simplification?

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

8(t+2) -3(t-4)=6(t-7)+8

or, 8t + 16 -3t +12 = 6t - 42 +8

or, 5t + 28 = 6t - 34

or, t = 62

Hence, The solution is, the value we get, t = 62.

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if gallup wishes to use a 95% confidence interval, compute the minimum number of american adults that they need to survey to ensure that the error bound, under no circumstances, is more than 0.01 before conducting the experiment?

Answers

the minimum number of american adults that they need to survey to ensure that the error bound is 16,867 with sample size

The sample size of a study is the number of subjects or observations that are included.Two statistical properties are influenced by the sample size: 1) The accuracy of our estimates, and 2) The ability to draw conclusions from the study.

The minimum sample size required to get a 95% confidence interval with an error bound of 0.01 is 16,867. This can be calculated using the formula:

n = (1.96 / 0.01)2 = 16,867.

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To test the effectiveness of a liquid supplement that is supposed to help forgetful people with their memory, 400 college students are recruited for a study and divided into two groups. Group A with 250 students receives the supplement, while group B with 150 students receives some colored water. Neither group is told what they received. After several weeks, they are given a memory test. This study can best be described as: . a census a controlled placebo experiment a survey using quota sampling a survey using simple random sampling the placebo effect

Answers

This study can be best described as Controlled Placebo Experiment

What is a Controlled Placebo Experiment?

A controlled placebo experiment is a type of research method that is used to check the effectiveness of a drug in a patient. This is done by selecting a sample group, then randomly divide the two group into a placebo group (this are the group that will receive the drug treatment ) and the controlled group (these are the group that will receive a colored mixture that looks like the drug, but does not have any effect). Without the groups knowledge about the real drugs and the colored mixture, but are followed up and tested.

According to the given question:

This is a controlled placebo experiment, because 400 student has been chosen as the sample, and are divided into a placebo group and a controlled group, to check the effectiveness of a drug on their memory.

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a laboratory supply company produces graduated cylinders, each with an internal radius of 222 inches and an internal height between 7.757.757, point, 75 inches and 888 inches. what is one possible volume, rounded to the nearest cubic inch, of a graduated cylinder produced by this company?

Answers

One possible volume of a graduated cylinder produced by the company is 98 cubic inch.

The volume of a cube is defined as the total number of cubic units occupied by the cube completely. A cube is a three-dimensional solid figure, having 6 square faces. Volume is nothing but the total space occupied by an object. An object with a larger volume would occupy more space.

The volume of a cube can be found by multiplying the edge length three times. For instance, if the length of an edge of a cube is 4, the volume will be 4³. The formula to calculate the volume of a cube is given as,

Volume of a cube = s³, where 's' is the length of the side of the cube.

Given in the question:

Radius of cylinder = 2 inches.

Height of the cylinder = 7.75 to 8 inches.

We know that,

Volume of Cylinder = πr²

For minimum Volume 7.75 :

                   Volume = πr²× 7.75

                                 = 3.14 × 4 × 7.75

                                 = 97.34 cubic inches.

For maximum volume 8.00 inches

                       Volume = πr² × 8

                                     = 3.14 × 4 × 8

                                     =  100.81

Therefore, the possible volume could be between 97.34 cubic inches and 100.81 cubic inches.

Thus, the volume is 98 cubic inches.

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An environmental group conduct a tudy to meaure energy conumption in a large metropolitan city a meaured by the amount of gaoline purchaed. In a random ample of 17 vehicle owner on a particular day, they calculated a mean of 13. 62 gallon and a tandard deviation of 4. 68 gallon. What i the tandard error of the ample mean?

Answers

The random sample study's standard error, which measures the energy usage in a major metropolis, is 0.275.

How is the standard error calculated?The standard deviation among the sample means is typically the standard error of a sampling distribution. It fluctuates inversely with sample size, meaning that as sample size rises, the sampling distribution's standard error falls.

The formula used to compute standard error is as follows:

standard error = standard deviation / √sample size

For  the data given in question-

In a random sample of 17 car owners on a given day, the mean fuel consumption was 13.62 gallons, and the standard deviation was 4.68 gallons.

Thus,

Standard error = 4.68 / 17

Standard error  = 0.275

Thus, the standard error for the mean of the sample is found as 0.275.

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If x = 6, what y? Please help

Answers

Answer: I think the answer is 2

Step-by-step explanation:

The smaller of the two shapes is 12, and the larger of the two shapes is 16,

I found that the difference between the two is 4 (or 16 - 12 =4). If x = 6 and the difference is 4, then subtract 4 from 6 and the answer will come out to be 2

16-12=6-4

y=2

Morgan and her children went into a grocery store and she bought $10
worth of peaches and mangos. Each peach costs $1 and each mango
costs $2. She bought a total of 8 peaches and mangos altogether.
Graphically solve a system of equations in order to determine the
number of peaches, a, and the number of mangos, y, that Morgan
bought.

Answers

Answer:

The number of peaches and the number of mangos that Savannah bought

are 4 and 10 respectively.

The variable use to write the equation is x and it is the number of peaches

Savannah and her children bought

let

the number of peaches Savannah and her children bought = x

Therefore

the number of mangoes Savannah and her children bought = x + 6

The total worth of what they bought = $22

Therefore,

1.75x + 1.50(x + 6) = 22

1.75x + 1.50x + 9 = 22

3.25x + 9 = 22

3.25x = 22 - 9

3.25x = 13

x = 13 / 3.25

x = 4

Therefore,

number of peaches bought = 4

number of mangoes bought = 4 + 6 = 10

Step-by-step explanation:

Answer: 6 Peaches and 2 Mangos

Step-by-step explanation: If one peach is worth $1 and one mango is worth $2, to get $10 used you need to buy 6 peaches and 2 mangos since 2 + 2 = 4 and 6 + 4 = 10

PLS HELP 50 pnts!!!!!!! giving brainliest!!! 1-4 (find the slope)
-attached pic
-unacceptable answers will result in 2 reports (2 warnings and the max is 3 then you will be banned)

Answers

Answer:

1) slope = 1/2 2) slope= -1 3)slope= 1/2 4) 5/4

Step-by-step explanation:

if you want y intercpt form

1) y=1/2x

2)y= -x-3

3) y= 1/2x-3.5

4) y= 5/4x - 1

the planning board members for a city are debating whether to build a new municipal parking garage. the parking garage would be funded by the revenue the city collects from its existing parking meters. since the board members insist that the parking garage cannot be funded by raising property taxes, the mean daily parking revenue collected must be greater than $1,200. a random sample of 35 days was selected, and the parking revenue collected in dollars was recorded. based on previous research, the board members assume that the population standard deviation is $196. the board conducts a one-mean hypothesis at the 1% significance level, to test whether the mean daily parking revenue is greater than $1,200.

Answers

The required hypothesis for the given data of the problem is  

Null hypothesis H₀: μ=$1200 , n = 35

Alternate hypothesis Hₐ : μ > 145

What is tailed test?

In statistics, a two-followed test is a technique wherein the basic region of a dissemination is two-sided and tests whether an example is more noteworthy or under a scope of values. It is utilized in invalid speculation endlessly testing for measurable importance.

According to question:

We have,

the board members insist that the parking garage cannot be funded by raising property taxes, the mean daily parking revenue collected must be greater than $1,200

So, Null hypothesis H₀: μ=$1200 , n = 35

Then, Alternate hypothesis Hₐ : μ > 145

Standard deviation = $196

Thus, It is right tailed hypothesis.

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If a building i 50 feet in diameter and you need 20 feet of clearance all the way around the building, how many feet of fence to you need to go around the building?

Answers

31.41 feet of fence to you need to go around the building.

What is circumference of a circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

The radius of the circle given is = 50/2 feet.

So the clearance of 20 feet will be there all way.

So total effective radius will be 25-20 5 feet.

the circumference is 2πr = 2*π*5 = 31.41 feet

Hence, 31.41 feet of fence to you need to go around the building.

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help plsssssssssssssss

Answers

Answer:

multiplication property of equality

a town’s january high temperatures average 36°f with a standard deviation of 10°, while in july the mean high temperature is 74° and the standard deviation is 8°. in which month is it more unusual to have a day with a high temperature of 55°? explain.

Answers

It is more unusual to have a high temperature of 55 degrees in July because the month's z-score is 2.375 standard deviations from its mean.

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean. Standard deviation is significant because it enables consumers to evaluate risk. Think about an investing strategy with a 10% average yearly return.

Here,

Calculations are attached in image.

A high temperature of 55 degrees is particularly rare since July's z-score is 2.375 standard deviations outside of its mean.

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In cooking class, Lupita and Jacob each make a mixture of basil and oregano. Lupita uses 2 tsp basil for every 3 tsp oregano. Jacob uses 4 tsp basil for every 5 tsp oregano. Lupita says the two mixtures will taste the same. Jacob says his will have a stronger basil taste than Lupita’s. Who is correct? Explain.

Answers

Using ratio and proportions, Jacob has mixture with stronger basil taste

Ratios and Proportion

Ratio can be defined as a comparison between two or more numbers that shows their sizes in relation to each other. A ratio often compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.

Proportion can be defined as equality of two ratios. Two equivalent ratios are always in proportion. Proportion is an equation or statement that shows that the two ratios or fractions are equivalent.

In this case, we can compare the ratio and determine which will have a stronger basil taste.

Lupita mixed 2 tsp of basil for 3tsp of oregano

The ratio of basil to oregano = 2/3 = 0.67

Jacob mixed 4 tsp of basil for 5 tsp of oregano

The ratio of basil to oregano = 4/5 = 0.8

Comparing the ratios, Jacob ratio is higher compared to Lupita and makes Jacob have the strong basil taste.

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samantha is considering job offers from two companies. company a offered her a starting salary of $48,000 with a $2100 raise at the end of each year. company b offered her a starting salary of $48,000 with a 3.7% raise at the end of each year.
Let f(t) represent Rosa's salary at Company A, t years after accepting a position at Company A, and let g(t) represent Rosa's salary at Company B t years after accepting a position at Company B.
Complete the table of values below:
t f(t) g(t)
0 50000 50000
1
2
3

Answers

The value of f(t) are 48000, 52200, 54300, 56400, and g(t) are 48000, 49776, 51617.71, and 53527.56.

She was given a starting wage of $48,000 from Company A, with annual raises of $2100.

The formula for Company A is

f(t) = 48000 + 2100t

She was given a starting wage of $48,000 from Company B, with an annual rise of 3.7%.

The formula for Company B is

g(t) = 48000 × [tex](1 + 0.037)^t[/tex]

The value of f(t) and g(t),

t ------- f(t) ------- g(t)

0 ----- 48000 ----- 48000

1 ------ 52200 ----- 49776

2 ----- 54300 ----- 51617.71

3 ----- 56400 ----- 53527.56

The graphical representation of both the linear equations of company A and company B.

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7x3/4=7 true or false

Answers

Answer:

false

Step-by-step explanation:

7*3 / 4 = 7

21 / 4 = 7

5.25 ≠ 7

Could you please give me brainliest? Thanks!

a research study reported that 10% of the people who are given a certain drug experience dizziness.if 15 people are selected at random, find the probability that none of them experience dizziness when given the drug.

Answers

Out of the 15 people the probability that none of the patients will experience dizziness is approximately 0.206 .

10% of the people experiences dizziness.

Probability that a random patient experiences dizziness = 0.1

Probability that the person does not experience dizziness = 0.9

Now this is in the form of a binomial distribution such that the probability is given by:

Sample = 15

P = 0.1

P' =0.9

Required probability :

= ¹⁵C₀ × P⁰ × P'¹⁵ (binomial distribution)

= 1 × 0.1⁰ × 0.9¹⁵

= 0.20589...

≈ 0.206

Hence the required probability is approximately 0.206 .

The binomial distribution is often used to predict the number of further successes in either a sample of size n drawn under replacement from either a population of size n.

If the sampling is carried out without replacement, the drawings are not independent, hence the resulting distribution is a hypergeometric one rather than a binomial one.

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in a lecture hall containing 100 people, you consider whether or not there are three people in the room who share the same birthday. explain how to calculate this probability exactly, using the same assumptions as in our previous analysis.

Answers

The probability of three people who share the same birthday is 0.6459.

Let us consider that A₀ be the event that everyone in the room has a distinct birthday. Let Ai be the event that pairs of people share a birthday. Then the probability we are interested in is

P(at lest three people share a birthday) = 1 - P(A₀) - ∑ P(Ai)

where there are n people in the lecture hall.

First we note that P(A₀) is in the book and is

P(A₀) = (365Cn)n!/365^n.

Now we will compute P(Ai).

For i = 1,

P(A₁) = (365) × [tex]\frac{(nC2)(365-1Cn-2)(n-2)!}{365^{n} }[/tex]

For i = 2,

P(A₂) = [tex]\frac{(365C2)(nC2)(n-2C2)(365-2Cn-4)(n-4)!}{365^{n} }[/tex]

This generalizes for i pairs of people sharing i distinct birthdays

P(Ai) = (365Ci)πj=1toi(n-2j+2C2)(365-iCn-2i)(n-2i)!/([tex]365^{n}[/tex])

Substituting all values into the equation and putting in n = 100, we can compute a value for this probability.

Therefore we get,

P(at least 3 people share a birthday)0.6459.

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can someone help me really quick


(please Explain how you know this is correct)

Answers

The answer is $12.50

You can see on the graph that if the weight is 20 pounds, it will cost $10. We are looking for how much it will cost to ship a 25 pound package. It can’t be $20.00 either.


hope this helps!

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for a list of five positive integers, none greater than 100, the mean is 1.5 times the mode. if 31, 58, 98, $x$ and $x$ are the five integers, what is the value of $x$?

Answers

The value of x from the given five integers is 34.

Here we have to find the value of x.

Data given:

Five positive number = 31, 58, 98, x, x

The mean is 1.5 times the mode.

Mean = (31 + 58 + 98 + x + x) / 5

         = (187 + 2x) / 5

Mode = x

As the mean is 1.5 times the mode so from this we have:

mean = 1.5 × mode

(187 + 2x)/ 5 = 1.5x

187 + 2x = 7.5x

5.5x = 187

x = 34

Therefore the value of x is 34.

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The base of a triangle is four more than twice its height. If the area of the triangle is 43 square centimeters, find its base and height.
The height of the triangle is
centimeters.
(Simplify your answer. Type an exact answer, using radicals as needed.)

Answers

The height of the triangle would be 5.63 cm.

What is the area of the triangle?

For a given triangle of height 'h' and the base is 'b' then the area of the triangle is

            A = 1/2 Base * Height

Given data:

          Base of the triangle = 2*height of the triangle + 4

                      b = 2h + 4

Area = 43 square centimeters

By using the area of the triangle,

        A = 1/2 *b * h

    43 = 1/2(2h + 4)*h

    86 = 2h²+4h

Simplifying this, we get

        h² + 2h - 43 = 0

Solving this, we get

h = 5.63 and h = -7.63

Height cannot be a negative value so h = 5.63

Hence, the height of the triangle would be 5.63 cm.

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on your desk, there is a very special die with a prime number p of faces, and you throw this die once. show that no two events a and b can be independent unless either a or b is the whole sample space or the empty set.

Answers

We have proven that no two events a and b can be independent unless either a or b is the whole sample space or the empty set below.

A sample space can be defined as the set of all possible outcomes of any experiment.

We are already aware that the outcomes of this die are going to be (1,2,3,..p). If we have a pair of proper events A, B which are independent, this would mean that = A∩B={∅}  (i)

This is a contradiction. So, now we suppose that = A∩B=C, for some proper event C (ii)

Using the values of (i) and (ii), we get -

= |C|p=P(A∩B)=P(A)P(B)=|A||B|p2.

= p|C|=|A||B|.

From this, we understand that neither A nor B are going to be full spaces and hence, no two events a and b are independent and 0<|A|<p and 0<|B|<p. Since |C| is also going to be less than 0 and p is prime, p divides either |A| or |B|.  if p was not prime (say, p=4), then you would only need the factors of p to divide either |A|,|B|, so, it becomes necessary for p to be a prime number. Hence, proved.

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Which of these relations is a function?

Answers

The relation that is a function is the graph (d)

How to determine the function?

From the question, we have the graphs to represent the given parameters that can be used in our computation

We are to find out which of them represents a function

For a graph to represent a function, the graph must pass the vertical line test

This means that a line drawn from the x-axis must touch the graph at most once

So, we draw these lines  and attach the graphs (see attachment)

The graph that pass the vertical line test is graph d

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the execution of the commandselect cname from customer where age < 30 and age > 40will produce the following number of rows:

Answers

The given command  "select cname from customer where age < 30 and age > 40" will produce 4 rows according to the database table.

What is database?

A database in computing is a structured collection of data that is electronically accessible and stored. Large databases are housed on computer clusters or cloud storage, whilst small databases can be kept on a file system. A database is a collection of data that has been organized to make it simple to maintain and update. Data records or files containing information, including as sales transactions, customer information, financial data, and product information, are often aggregated and stored in computer databases. A database is a planned gathering of data. They enable the manipulation and storage of data electronically. Data administration is made simple by databases. Let's use a database as an example. A database is used to store information about people, their phone numbers, and other contact information in an online telephone directory.

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Help please!! I need this answer!!​

Answers

Answer: Store B and C sell at a lower unit price.

Step-by-step explanation:

Store B: $3.48/3 = $1.16 per pound.

Store C: $3.80/4 = $0.95 per pound.

the residual is defined as the difference between the actual and predicted, or fitted values of the response variable. group of answer choices false true

Answers

The Residual is defined as the difference between the actual and predicted, or fitted values of the response variable. This statement is true.

Linear regression is a statistical tool that determines how well a straight line fits a set of paired data. The straight line that best fits that data is called the least squares regression line. This line can be used in a number of ways. One of these uses is to estimate the value of a response variable for a given value of an explanatory variable. Related to this idea is that of a residual.

Residuals are obtained by performing subtraction. All that we must do is to subtract the predicted value of y from the observed value of y for a particular x. The result is called a residual.

The formula for residuals is straightforward:

Residual = observed y – predicted y

It is important to note that the predicted value comes from our regression line. The observed value comes from our data set.

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a population doubles in size every 15 years. assuming exponential growth, find the (a) annual growth rate (b) continuous growth rate

Answers

The annual growth rate is 4.73 %

The continuous growth rate is 4.62 %

What is exponential growth function ?

A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.

Let us assume:

The initial amount of 1, so results are 2.

Let x be the  percent in decimal form

Growth rate per year:

[tex]1(1+x)^{15} = 2[/tex]

Take ln on both the sides

[tex]ln((1+x)^{15}) = ln(2)[/tex]

15*ln(1+x) =0 .693

ln(x+1) = 0.693/15

ln(x+1) = 0.04621

Take anti ln on both the sides

x+1 = 1.0473

x = 1.0473 - 1

x = .0473

x =4.73 % annual growth rate

Continuous growth rate:

[tex]1*e^{15x} = 2[/tex]

[tex]ln(e^{15x}) = ln(2)[/tex]

15x*ln(e) = ln(2)

ln(e) = 1

15x =0.693

x =0 .693/15

x = .0462

x = 4.62 %

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