If an initial amount A0 of money is invested at an interest rate i compounded times a year, the value of the investment after t years is If we let n = 8, that is referred to as the continuous compounding of interest. Use L' Hospital's Rule to show that if interest is compounded continuously, then the amount after years is A=A0eit
Answers
Answer:
Following are the solution to the given point:
Step-by-step explanation:
Please find the comp[lete question in the attached file.
Given:
[tex]\bold{ \lim_{n \to \ \infty} (1+ \frac{r}{n})^{nt} =e^{rt}}[/tex]
In point 1:
[tex]\to y = (1+ \frac{r}{n})^{nt}[/tex]
In point 2:
[tex]\to \ln (y)= nt \ln(1+ \frac{r}{n})[/tex]
In point 3:
Its key thing to understand, which would be that you consider the limit n to[tex]\infty[/tex], in which r and t were constants!
[tex]=lim_{n \to \ \infty} \ln (y) = lim_{n \to \ \infty} nt \ln(1+\frac{r}{n})\\\\= lim_{n \to \ \infty} \frac{\ln(1+\frac{r}{n})}{\frac{1}{nt}}\\\\= lim_{n \to \ \infty} \frac{\frac{-r}{\frac{n^2}{(1+\frac{r}{n})}}}{- \frac{1}{n^2t}}\\\\= lim_{n \to \ \infty} \frac{\frac{rn^2t}{n^2}}{(1+\frac{r}{n})}\\\\= lim_{n \to \ \infty} \frac{rt}{(1+\frac{r}{n})}\\\\= \frac{rt}{(1+\frac{r}{0})}\\\\=rt[/tex]
In point 4:
[tex]\to \lim_{n \to \ \infty} = (1+\frac{r}{n})^{nt}[/tex] and
[tex]\to \lim_{n \to \ \infty} = A_0e^{rt}[/tex]
Related Questions
Michael’s $1200 car insurance is paid bi-yearly. The second payment is three times the first payment. Find the amount of the first and second payment.
Answers
300x 3 =900 second year
Evaluate -3- (-4) - (-2) + 1.
Answers
Answer:
4
Step-by-step explanation:
-3+4+2+1=4
2. Write a quadratic function given the roots (4,0) and (2, 0) and the point 2 points
(3, 4). (2 pts) *
Answers
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]y = -4(x - 2)(x - 4) [/tex]
[tex]y = -4 {x}^{2} + 24x - 32 [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
The expression for the quadratic function will be y = -4x² + 24x - 32.
What is a quadratic equation?A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given that a quadratic function given the roots (4,0) and (2, 0). The quadratic equation will be formed as below:-
The two roots of the quadratic equation are 2 and 4 then the two factors will be ( x- 2 ) and ( x - 4).
y = -4(x-2)(x-4)
y = -4x² + 24x - 32.
Therefore, the expression for the quadratic function will be y = -4x² + 24x - 32.
To know more about quadratic equations follow
https://brainly.com/question/1214333
#SPJ5
System of Equations in Three Variables Word Problem
Answers
Answer:
i think the answer is a number or multiple number and maybe a decimal.
Step-by-step explanation:
go to Tiger Algebra Solver
What is mA?
Enter your answer in the box.
Answers
Answer:
X=3.75
Step-by-step explanation:
A=24.25
I guess
George, a musician, works 35 hours in a week. If he earns $18.15 per hour, how much does he earn each week?
Answers
Answer:
$635.25
Step-by-step explanation:
He works 35 hours a week, multiply that by $18.15 and you get $635.25.
Can someone help me? Please i need this done
Answers
ratio of 5 to 2 total number of servers and cooks is 42 how many servers
Answers
Answer:
30
Step-by-step explanation:
5 x 6 = 30
2 x 6 = 12
30+12 = 42
Find the other endpoint of the line segment with the given
endpoint and midpoint: Midpoint = (8,-2) and Endpoint= (3,10).
Answers
Answer:The other endpoint is at ( − 4 , 3 )
Explanation:
The line segment passing through ( − 4 , 9 ) and ( − 4 , 6 )
is a vertical line with the midpoint 3
units below the first point.
The other endpoint must be 3
further units below the midpoint i.e. at ( − 4 , ( 6 − 3 )
Step-by-step explanation:
Free Brainlyest for who says bababoi first
Answers
Answer:
bababoi .. yay I did something
Answer:
bababoi
Step-by-step explanation:
bababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoivbababoibababoibababoibababoibababoibababoibababoibababoivbababoibababoibababoibababoibababoibababoibababoibababoioibababoibababoivbababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoibababoi
What is the blank answer?
Answers
Answer:
you.. need to provide a picture
Step-by-step explanation:
If a/b and x/y represent rational expressions and b0 and y0, what is true of their product? Select three options.
The product is equivalent to ay/bx
The product is a rational expression.
The product is equivalent to a/y(x/b)
The product is the ratio of ax and by.
The product is equivalent to ax/b(y)
Answers
Answer:
It’s the 2nd,3rd,and 4th
Step-by-step explanation:
I just took the quiz
Answer:
2,3,4
Step-by-step explanation:
What is the percent?
32/80 = %/100
Answers
Answer: 40% OUT OF 100
definitonss for math really easy
Answers
Answer:The solution to a system of linear equations is the point at which the lines representing the linear equations intersect. Two lines in the x y xy xy -plane can intersect once, never intersect, or completely overlap.
A system of linear equations is usually a set of two linear equations with two variables. x + y = 5 x+y=5 x+y=5x, plus, y, equals, 5 and 2 x − y = 1 2x-y=1 2x−y=12, x, minus, y, equals, 1 are both linear equations with two variables. When considered together, they form a system of linear equations.
a numerical or constant quantity placed before and multiplying the variable in an algebraic expression.
a constant term is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables. For example, in the quadratic polynomial the 3 is a constant term.
Step-by-step explanation:
1
Which equation has a constant of proportionality equal to1/2
Choose 1 answer:
Answers
Answer:
C
Step-by-step explanation:
3/6 = 1/2 when simplified.
Divide the binomial by the monomial to find the quotient.
Answers
Answer:
9x²-36[tex]y^{5}[/tex]
Step-by-step explanation:
Explain how to find the slope of the line. And explain answer
Answers
Answer:
by using the slope incercept form: y=mx+b
this one is m=7/3 (m is the letter we use for the word slope btw) :)
Step-by-step explanation:
3.55. Постройте график линейной функции:
1) у = 2/3х – 4;
2) y = 2x + 6;
3) у = -1,5х – 3;
4) y = -1/2x + 1;
5) y = 5/3x - 2;
6) y = -4/3x + 2;
Answers
Answer:
4) y = -1/2x + 1;
Step-by-step explanation:
maybe
or maybe not
Which equation has a constant of proportionality equal to 1/2?
Answers
Answer:
y=1/2x or y=.5x
Step-by-step explanation:
Example of a balance point
Answers
a home's loss of heat is equal to heat created in the home or when both sides of a seesaw are at an equal level.
(5x + 2) 6x
Solve for x and y
X =
y =
Answers
Answer:
x = 8
y = 138
Step-by-step explanation:
unit 8 right triangles and trigonometry homework 1
Answers
Answer:
x = 31.8
Step-by-step explanation:
From the picture attached,
By applying Pythagoras theorem in right ΔADC,
AC² = AD² + CD²
(22)² = AD² + (16)²
AD² = 484 - 256
AD = √228
= 2√57
Now we apply Pythagoras theorem in right ΔADB,
AB² = AD² + DB²
x² = 228 + (44 - 16)²
x² = 228 + 784
x² = 1012
x = √1012
= 31.81
≈ 31.8
The side x is an hypotenuse side to one of the right triangles formed by
altitude of the given triangle that has solid lines.
x is approximately 31.812
Reasons:
The figure shows a triangle with an altitude that forms two triangles inside
the main triangle.
By Pythagoras's theorem, we have;
For the right triangle on the left;
22² = h² + 16²
h² = 22² - 16² = 228
h² = 228
h = √228 = 2·√57
h = 2·√57
In the right triangle to the right, we have;
The length of the top base, b = 44 - 16 = 28
The square of the hypotenuse, x² = h² + b²
∴ x² = 228 + 28² = 1012
x = √(1012) = 2·√253
x = 2·√253 ≈ 31.812
Learn more here:
https://brainly.com/question/6241683
I need help solving this
Answers
Answer:
It's D.
Step-by-step explanation:
31-4 = 27 , 63 + 27 = 90 :) so the answer's D. 31
Answer:
D) 31
Step-by-step explanation:.
It is a right angle. All right angles equal 90°. So the two angles add up to 90
90= 63 + x - 4
Add 4 to each side
94 = 63 + x
Subtract 63 to each side
31 = x
The following measurements were added: 5.45 + 6.1 + 2.84. what should
the answer be reported as *
1)14.39
2)14.3
3)14.4
4)14
Answers
Explanation:
5.45+2.84= 8.29
Then for 6.1 you add a zero to the end and make it 6.10 which is the same thing
Now 8.29+6.10= 14.39
For what value of b, would the equation 34(12x−9)+b4=5−3(2−3x) have infinitely many solutions?
Answers
Answer:
23
Step-by-step explanation:
7) Newton sees 50 frogs in the morning, and 7 fewer frogs in the
afternoon. How many frogs did he see in total?
Answers
Answer:
93
Step-by-step explanation:
These two triangles are similar. What are a and b? Note: the two figures are not drawn to scale. Please help with this!!!
Answers
9514 1404 393
Answer:
a = 6b = 22.5Step-by-step explanation:
The ratio of smallest sides in the two triangles is ...
smaller / larger = 4/10
To find A and B, we write proportions involving corresponding side lengths.
__
Side A in the smaller triangle is ...
A/15 = 4/10
A = (4/10)(15) = 6
__
The ratio of larger to smaller is the inverse of the above ratio, so ...
B/9 = 10/4
B = (10/4)(9) = 22.5
A pet shelter maintains a ratio of 5 cats to 8 dogs. If there are 117 total animals in the shelter, how many are dogs? Set up and solve a proportion.
Answers
Show how to find the following product using a diagram
1/4 × 2/3
Answers
Answer:
3/3
Step-by-step explanation:
Help plssssssssssssssss
Answers
Answer:
less than 5
Step-by-step explanation:
im pretty sure