The formula A = Pe^rt calculates the amount an investment earning a nominal rate of r compounded continuously is worth. Show that the amount of time it takes for the investment to double in value is given by the expression ln2/r.

Answers

Answer 1

Answer:

t = In2/ r

Step-by-step explanation:

Given the formula : A = Pe^rt

For investment to double ;

Final amount (A) = 2 * initial investment (p)

A = 2p

Hence,

2p = pe^rt

2 = e^rt

Take the In of both sides

In2 = rt

Divide both sides by r

In2 /r = rt /r

In2/ r = t

t = In2/ r ; Hence, the proof

Answer 2

The formula for obtaining the time taken when the amount is double the principal is ln2/r.

Given that;

A = Pe^rt

A = amount

P = principal

r = rate

t = time

Now we are told that;

A = 2P

Hence;

2P = Pe^rt

2 = e^rt

ln 2 = rt

t = ln2/r (QED)

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Related Questions

What is 15 % converted into numbers, or 120$ increased by 15%

Answers

$120 increased by 15% is 138.00

I will mark you brainliest

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Answer:

Hope this helps, happy learning!!!

PLease help me for my homework hahaqhahahahahhahaha please

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Answer

Step-by-step explanation:

rise over run so it'd be 3/3 positive or y= 3x-3

Question: If an electric train is moving north at 100mph and a wind is blowing to the west at 10mph, which way does the smoke blow?

Answers

Answer:

There is no smoke due to it being an electric train.

Step-by-step explanation:

Didn't fool me. ;)

that question has already been answered: https://brainly.com/question/4480585

Bonus (3 points)
Graph the parabola using the indicated information (you may NOT use decimals) You must show all work to
receive credit.

y = 2^2 + 17x +30

a. equation of the axis of symmetry

b. coordinates of the vertex

c. calculate the coordinates of the x-intercepts

Answers

Answer:

c

Step-by-step explanation:

−4y−4+(−3)
is anyone on that can help with this question I'm an idiot and can figure it out please help

Answers

Answer:

soln

-4y-4-3

-4y-7

- (4y+7)

Explain what is happening at this step in the solving equation process.

1. 10 − 6 x = 4 + 5 x

2. 7-6x=1+5x

Answers

Answer:

1. After solving we get value of x: [tex]\mathbf{x=\frac{6}{11} }[/tex]

2. After solving we get value of x: [tex]\mathbf{x=\frac{6}{11} }[/tex]

Step-by-step explanation:

We need to Solve the equations.

1.  [tex]10 - 6 x = 4 + 5 x[/tex]

Step 1: Subtract 5x on both sides

[tex]10 - 6 x-5x = 4 + 5 x-5x\\10-11x=4[/tex]

Step 2: Subtract 10 on both sides

[tex]10-11x-10=4-10\\-11x=-6[/tex]

Step 3: Divide both sides by -11

[tex]\frac{-11x}{-11}=\frac{-6}{-11}\\x=\frac{6}{11}[/tex]

So, after solving we get value of x: [tex]\mathbf{x=\frac{6}{11} }[/tex]

2. [tex]7-6x=1+5x[/tex]

Step 1: Subtract 5x on both sides

[tex]7 - 6 x-5x = 1 + 5 x-5x\\7-11x=1[/tex]

Step 2: Subtract 7 on both sides

[tex]7-11x-7=1-7\\-11x=-6[/tex]

Step 3: Divide both sides by -11

[tex]\frac{-11x}{-11}=\frac{-6}{-11}\\x=\frac{6}{11}[/tex]

So, after solving we get value of x: [tex]\mathbf{x=\frac{6}{11} }[/tex]

Which value shows the constant of proportionality for the equation y = 15x?
y
15
x
15x

Answers

Answer:

Step-by-step explanation:

15x because its not multiplying or dividing or adding and subtracting

A driver receives -25 points for a rule violation. What integer represents the change in points after four rule violations?

Answers

Answer:

It would be -100

Given: a and b are parallel and c is a transversal. Prove: ∠2 ≅ ∠7 Parallel lines b and a are cut by transversal c. On line b where it intersects with line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 5, 6, 2. On line a where it intersects with line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 3, 7, 8, 4. Use the drop-down menus to complete the paragraph proof showing that alternate interior angles are congruent. We know that lines a and b are parallel and that line c is a transversal because that is given. We can tell that angles 2 and 5 are congruent because angles are congruent. Angles 5 and 7 are congruent because angles by parallel lines cut by a transversal are congruent. Therefore, angles 2 and 7 are congruent based on the

Answers

Answer: vertical,corresponding,transitive property

Step-by-step explanation:

Answer:

vertical

corresponding

transitive property

Step-by-step explanation:

just took the test

3/5 + 1/2 in simplest form

Answers

Make them common denominator
3/5 = 6/10
1/2 = 5/10
6/10 + 5/10 = 11/10 = 1 1/10

Simplified it would be [tex]\frac{11}{10}[/tex].

32x+8+5=113 2x+8 +5=11 simplify in radical form

Answers

Answer:

The answer is in the picture below

Step-by-step explanation:

The Lugar family spends spring break camping. The campground charges a $5 entrance fee plus $10 per night to camp in the park. Which of the following graphs best represents the relationship between the number of nights the Lugar family camps and the cost?

Answers

Answer:

(0,5) , (1,15) , (2,25) , (3,35) , (4,45) {the cords for the answer because it might be different for you. Also this is not a straight line they are dots.

Step-by-step explanation:

For one night, you have to pay $5 for an entry fee, and $10 for a night. Which means its $15 for one night. This increases every night.

m = ab + 3c Solve for a

Answers

Answer:

[tex]\frac{M-3c}{b}=a[/tex]

Step-by-step explanation:

[tex]M=ab+3c\\M-3c=ab\\\frac{M-3c}{b}=a[/tex]

Answer:

[tex]\frac{m - 3c}{b} = a[/tex]

Step-by-step explanation:

m = ab + 3c

-3c        - 3c

m - 3c = ab

[tex]\frac{m - 3c}{b} = \frac{ab}{b}[/tex]

[tex]\frac{m - 3c}{b} = a[/tex]

I WILL MARK BRAINIEST
please answer question 4
It shows the one I got wrong so please don’t choose that one

Answers

Answer:

C is the correct one.

Step-by-step explanation:

You can find answer by RHS rule of congruency.

RHS stands for Right angle, Hypotenuse, and Side

Answered by,

Z.Khan,

India

How do I work out 5 divided by 102.05???
Thanks to kasey1476443 for giving me the answer. She is a HERO!!!
I have one question how do I work out 5 divided by 102.05? You can add a picture when you comment.

Answers

Answer:

0.04899559039

Step-by-step explanation:

I put it in the caculator

Answer: The answer is 20.41

Step-by-step explanation:

After the semester is over, you discover that the math department has changed textbooks (again) so the bookstore won't buy back your nearly-new book. You and your friend Anna decide to get creative. You go to the rook of a five-story building and look over the edge to the reflecting pool 60 feet below. You drop your book over the edge at the same instant that Anna chucks her book straight down at 30 feet per second. By about how many seconds does her book beat yours into the water (approximately)? Your function is s(t)=−16t2+60 Anna's function is s(t)=−16t2−30t+60

Answers

Answer:

0.78 s

Step-by-step explanation:

Since the position of the pool is at 60 feet below, s(t) = -60 for both me and Anna. So, both expressions for the motion of the book are equated to -60 and then solved to find the time they reach the water.

So, For me s(t)= −16t² + 60

-60 = −16t² + 60

collecting like terms, we have

-60 - 60 = −16t²

- 120 = −16t²

dividing both sides by - 16, we have

t² = -120/-16

t² = 7.5

t = √7.5

t = 2.74 s

For Anna, s(t)= −16t² - 30t + 60

-60 = −16t² - 30t + 60

adding 60 to both sides, we have

-60 + 60 = −16t² - 30t + 60 + 60

−16t² - 30t + 120 = 0

dividing through by -2, we have

8t² + 15t - 60 = 0

Using the quadratic formula to find t

[tex]t = \frac{-15 +/- \sqrt{15^{2} - 4 X 8 X -60} }{2 X 8} \\t = \frac{-15 +/- \sqrt{225 + 1920} }{16} \\t = \frac{-15 +/- \sqrt{2145} }{16} \\t = \frac{-15 +/- 46.31}{16} \\t = \frac{-15 - 46.31}{16} or t = \frac{-15 + 46.31}{16} \\t = \frac{-61.31}{16} or t = \frac{31.31}{16} \\t = -3.83 s or 1.96 s[/tex]

Since t' cannot be negative, t' = 1.96 s.

It takes Anna's book 1.96 s to reach the water, while it takes 2.74 s for my book to reach the water.

So, the time it takes Anna's book to beat mine is the difference between the time of reaching the water of each book. So Δt = t - t' = 2.74 s - 1.96 s = 0.78 s

how do you write 564,000,000 in scientific notation

Answers

Answer:

5.64 x 10 x 8

Step-by-step explanation:

Answer:

5.64 x 10^8

Step-by-step explanation:

since it is a positive number, you’d start the decimal at the beginningeaning the right of the number) and move it all the way to the second to last number to the left. How many times you move the decimal is the exponent.

what is halfway between 5.3 and 5.4

Answers

Answer:

5.3 1/2

Step-by-step explanation:

jaleia borrows $1500 from the bank. To pay back the loan this year, she will pay the bank the amount she borrowed plus 12% simple interest. Jaleia wants to know the total amount she will pay back
[tex]y \\ [/tex]

Answers

Answer:

asdfasdf

Step-by-step explanation:

Answer:

$1680

Step-by-step explanation:

1500=100%

100+12(interest)=112

112=1.12(multiplier)

1500×1.12=$1680

Ella is making beaded bracelets to sell at a craft fair. It takes 76 inches of string to make 19 bracelets.

Answers

The Answer:

The Cop= 4

What’s the value of p? Just type in the answer!!!

Answers

Answer:

The interior angles of any triangle equal 180.

This is an iscocleles triangle meaning p and i or the base angles are equal.

With those rules we see that 48°+p+I=180

p+I=132

132/2=66

therefore P and I equal 66

P=66°

Step-by-step explanation:

Helps me solve this problem please

Answers

Answer:

0,2

Step-by-step explanation:


4 ) Here is an explanation that the angle sum of triangle ABC is 180º.
The reasons for each line are missing.
Give the reasons.
1. Angle A of the triangle = angle PCA
2. Angle B of the triangle = angle QCB
3. Angle PCA + angle C of the triangle + angle QCB = 180°
Hence angle A + angle B+ angle C = 180°​

Answers

Answer:

Thank you and please rate me as brainliest as it will help me to level up

Find the values of x and y by writing two equations and solving the system of equations.

Answers

Answer:

y=2 x=5

Step-by-step explanation:

3x-2y=11

2x-3y=4

you multiply both equations to cancel one variable out. in this case you multiply the first equation by 2 and the second by -3

     6x-4y=22

+    -6x-9y=12

--------------------------

0x+5y=10

y=2

you plug that in either equation

3x-2(2)=11

3x-4=11

3x=15

x=5

Dale will run at most 29 miles this week. So far, he has run 17 miles. What are the possible numbers of additional miles he will run?
Use t for the number of additional miles he will run.
Write your answer as an inequality solved for t.

Answers

Answer:

17+t=19

Step-by-step explanation:

there u go buddy :(

101.101 correctly written out in words

Answers

Answer:

One hundred one and one hundred one thousandths

Step-by-step explanation:

Answer:

Step-by-step explanation:

basicliy he's saying c

wich is true:)

3/4

(x−12)=12

will mark brainlyest

Answers

Answer:

x = 24, if thats wat ur asking.

Answer:

x = 28

Step-by-step explanation:

its division come on

Which word describes the slope of the line?
o positive
O negative
O zero
undefined

Answers

i’m not to sure my my guess is zero because it is not going up or down

How do I do 3 x 10^5

Answers

Answer: 3(10^5)

=3*10^5

=3*(10*10*10*10*10)

=300000

This is how you should do It, just when it is squared you should times the number like up here you times 10 times 10 5 times so if you see it you don't times it by 5 you do 10 times 10 times 10 times 10 times 10 like this

You should get it now

Have a good day

Yours,

Nathaniel

Step-by-step explanation:

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