PLEASEEEEE HELP…
In Exploration 3.1.2 you went through a procedure that helped you see how a formula
with n compounds per year relates to the formula for compounding continuously. Select
the appropriate answers to model what you did in the exploration.
Annual growth Rate
A (t) = P(1 + r)
n compounds per year
nt
A () = (1+ a)
a =
[Select]
n
let z = -
7
A (t) = P(1 + [b])"
b = (Select)
let n = ar
Ict
C =
[Select)
A (0) P(1)
110) - P{(x - 2)
+
2
Answers
The growth amount is given by the growth rate the duration of the growth
and how the rate is applied to each period.
The correct selections are;
a = n[tex]\displaystyle b = \frac{1}{x}[/tex]c = x·r[tex]\displaystyle \lim_{x \to \infty} \left(1 + \frac{1}{x} \right)^x \to 1[/tex]Reasons:
First part;
The given formula for the annual growth rate is; [tex]A(t) = \mathbf{P \cdot \left(1 + r)^t}[/tex]
[tex]\displaystyle A(t) = \mathbf{P \cdot \left (1 + \frac{r}{[a]} \right)^{n \cdot t}}[/tex]
Where;
P = The principal
r = The rate per period
n = The number of compounding per period
t = The number of periods
In the above formula, we have that the number of compounding per periods = n
Therefore;
a = nWhich gives the fraction of the interest applied to each period as [tex]\displaystyle \frac{r}{n}[/tex]
Which gives;
[tex]\displaystyle A(t) = \mathbf{P \cdot \left (1 + \frac{r}{n} \right)^{n \cdot t}}[/tex]
Second part;
When [tex]x = \displaystyle \frac{n}{r}[/tex], we have; [tex]A(t) = \mathbf{P \cdot \left(1 + [b])^{n \cdot t}}[/tex]
[tex]\displaystyle A(t) = P \cdot \left (1 + \frac{r}{n} \right)^{n \cdot t}[/tex]
Therefore;
[tex]\displaystyle b=\frac{r}{n}[/tex]
[tex]\displaystyle \frac{1}{x} = \frac{1}{\left(\frac{n}{r} \right)} =\frac{r}{n}[/tex]
Which gives;
[tex]\displaystyle b=\frac{r}{n} = \mathbf{\frac{1}{x}}[/tex]
[tex]\displaystyle \underline{ b = \frac{1}{x} }[/tex]
Third part;
Where, n = x·r, and [tex]\displaystyle A(t) = \mathbf{P \cdot \left (1 + \frac{1}{x} \right)^{[c] \cdot t}}[/tex]
We have;
[tex]\displaystyle x= \frac{n}{r}[/tex]
[tex]\displaystyle \frac{1}{x}=\frac{r}{n}[/tex]
[tex]\displaystyle A(t) = P \cdot \left (1 + \frac{1}{x} \right)^{[c] \cdot t} = \mathbf{P \cdot \left (1 + \frac{r}{n} \right)^{[c] \cdot t}}[/tex]
Which gives;
c = n = x·r
c = x·rFourth part;
If x is a really large number, we have; [tex]\displaystyle \mathbf{\left(1 + \frac{1}{x} \right)^x}[/tex]
Where x approaches ∞, we have;
[tex]\displaystyle \frac{1}{\infty}=0[/tex]
Which gives;
[tex]\displaystyle \displaystyle \left(1 + \frac{1}{x} \right)^x= \left(1 + \frac{1}{\infty} \right)^\infty = \displaystyle \left(1 + 0\right)^\infty = 1 ^\infty = 1[/tex]
[tex]\displaystyle \underline{\lim_{x \to \infty} \left(1 + \frac{1}{x} \right)^x \to 1}[/tex]Learn more about growth rate formula here:
https://brainly.com/question/2284816
Related Questions
A bowling special costs $8.50 per hour for each adult and $5.00 per hour for each child one adult and two children go bowling what is the equation that shows the relationship between cost In dollars and time
Answers
Answer:22$
Step-by-step explanation:
2x8.50 = 17+5 = 22$
How long do they bowl
bob's tire outlet sold a record number of tires last month . one salesman sold 165 tires
which was 60% of the tires sold in the month what was the record number of tires sold
Answers
Answer: 275 tires
Step-by-step explanation:
0.60X = 165 [One salesman sold 60% of the tires sold. X is the tires total sold]
X = 275 tires
If one piece of furniture was sold every 3/4 hour, how many pieces of furniture are sold in 3 hours
Answers
Answer:
Two pieces of furniture.
Step-by-step explanation:
3 hours times 1 piece of furniture every 3/4 hours:
3 · [tex]\frac{3}{4}[/tex] = [tex]\frac{3*3}{4}[/tex] = [tex]\frac{9}{4}[/tex] = 2.25
Assuming that pieces of furniture cannot be sold in parts, 2 whole pieces of furniture will be sold in 3 hours.
3 pounds of peanuts for $7. 50. How much is the cost per pound?.
Answers
7,50 divided by three
The dimensions of a carriage are:
height = x + 3 feet, length = 10x + 5 feet, and width= 2x-1 feet. If the volume of the carriage is 1050 cubic feet, what is the value of x?
Answers
Answer:
Step-by-step explanation:
length * width * height = 1050 cubic ft
(10x + 5)* (2x -1) * (x +3) = 1050
(10x + 5 )(2x-1) = 10x*(2x - 1) + 5*(2x -1)
= 10x*2x - 10x*1 + 5*2x - 1*5
= 20x² - 10x + 10x - 5 = 20x² - 5
(10x + 5)(2x -1)(x+3) = (20x² -5) *(x + 3)
=20x²*(x +3) - 5*(x +3)
= 20x³ + 60x² - 5x - 15
20x³ + 60x² - 5x - 15 = 1050
20x³ + 60x² - 5x - 15 - 1050 = 0
20x³ + 60x² - 5x - 1065 = 0
By trial and error method , (x -3 ) is a factor
Synthetic method:
3 ( 20 60 -5 -1065
( 60 360 1065
20 120 355 0
20x² + 120x + 355 = 0
Divide the equation by 5
4x² + 24x + 71 = 0 . Solving this equation gives imaginary number. So, ignore these values.
So, value of x = 3
height = 3+ 3 = 6 ft
Length = 10*3 + 5 = 30 + 5 = 35ft
Width = 2x - 1 = 2*3 - 1 = 6 - 1 = 5 ft
Check: length * width * height = 35 * 5 * 6 = 1050 cubic ft
what is the LCM of 900 and 30000
Answers
Answer: 90,000
To find the LCM (Least Common Multiple) of a number, list the multiples of each number.
Multiples of 900
Since they're a lot, we will extend it to the short version.
900, 2700, 9900, 37800, 85500, 90000
Multiples of 30000
30000, 60000, 90000, 120000, 150000
Looking at both multiples, the least common multiple is 90000, as it is listed in both 900 and 30000.
Hence, 90,000 is the answer.
In AWXY, X = 32 inches, y = 96 inches and ZW=16°. Find the area of AWXY, to the
nearest square inch.
Answers
Answer:
the nearest square inch is 50
I wmat to sleep been doing work for an hour help me out
Answers
Answer:
A. 23, 37.....
B. 26, 42......
Step-by-step explanation:
have a great day!
ANSWER QUICKLY
will give brainliest
Answers
Answer:
i only have 1
Step-by-step explanation:
Answer: Ok
Step-by-step explanation:
True or False: The U.S. Bureau of the Census provides information that is useful for defining the denominator in rates.
Answers
Answer:
True
Step-by-step explanation:
The unit circle has a radius of 1 unit and is centered at the origin. It is dilated so that it passes through the point (4, 0). What is the scale factor of dilation? 3 4.
Answers
Dilation involves changing the size of a shape (i.e. a circle)
The scale of dilation is 4
The circle passes through the origin.
So, one of the points is (0,0)
When dilated it passes through the point (4,0).
The scale factor (k) is calculated by calculating the distance between the new point and the old point.
So, we have:
[tex]\mathbf{k = \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}}[/tex]
This gives
[tex]\mathbf{k = \sqrt{(4- 0)^2 + (0-0)^2}}[/tex]
Simplify
[tex]\mathbf{k = \sqrt{16 +0}}[/tex]
Add 16 and 0
[tex]\mathbf{k = \sqrt{16}}[/tex]
Take the square root of 16
[tex]\mathbf{k =4}[/tex]
Hence, the scale of dilation is 4
Read more about dilation at:
https://brainly.com/question/13176891
HELPPPPPP PLSSSSSSSSS
Answers
Answer:
I can even see anything can you reupload your answer, please?
Step-by-step explanation:
Given, ∠POR=120
o
Hence, ∠POR=2∠PQR (half angle property)
∠PQR=
2
1
×120
o
=60
o
PQRS is a cyclic quadrilateral
∴∠PQR+∠PSR=180
o
∠PSR=180−60
∠PSR=120
o
The table shows the decay rate for a certain radioactive material over time. In this context, what does the y-intercept represent?
At 100 hours, there are 0 grams of the substance remaining.
At 100 hours, there are 100 grams of the substance remaining.
At 0 hours, there are 100 grams of the substance remaining.
At 0 hours, there is 1 gram of the substance remaining.
Answers
Answer:
At 0 hours, there are 100 grams of the substance remaining.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
I just did it on ed
what is the value of x that makes this equation true 3/4 + x = 1/8
Answers
The correct value of ''n'' in this equation will be -5/8.
Step-by-step explanation:To solve this equation, we're going to isolate ''x'', and then we're going to subtract the two fractions.
But to subtract the two fractions with different denominators, let's represent the fractions with the least common multiple of the denominators, being 8.
Resolution:[tex]\large \sf \dfrac{3}{4} +x=\dfrac{1}{8}[/tex]
[tex]\large \sf x= \dfrac{1}{8} -\dfrac{3}{4}[/tex]
[tex]\large \sf x= \dfrac{1-6}{8}[/tex]
[tex]\large \sf x= \dfrac{-5}{8}[/tex]
[tex]\boxed{\boxed{{\large \sf x=-\dfrac{5}{8} }}}[/tex]
So we can conclude that the value of ''x'' in this equation will be -5/8.
Jordan will hike a trail with the distance of 25 miles at a rate of 5 miles per hour. Write a linear equation to represent the distance Jordan still has to walk after x hours. What does the y-intercept of the equation represent?
Answers
Answer:
y = - 4 x + 20
Step-by-step explanation:
The trail is 20 miles
Each hour you go 4 miles, so you subtract that each hour
if 3/ 4 part of the total number of students in a class are girls how much percent are boys
Answers
Answer:
1
Step-by-step explanation: because 3 are girls and 3 + 1 equals 4 its 1
Answer:
1/4 or 25% are boys
Step-by-step explanation:
3/4 + 1/4 = 4/4
75% + 25% = 100%
solve pls brainliest
Answers
because its cubed
Answer:
64in
Step-by-step explanation:
v=L×W×H
= 4×4×4
= 16 ×4
= 64in²
Here you go ☺️ I NEED HELP SO HELP PLS
Answers
Answer:
the information above is not suffi
Step-by-step explanation:
hope it helps if wrong sorry
Answer:
The median height for tree 1 is greater.
Step-by-step explanation:
The height of tree 1 is greater therefore I believe the median will also be greater. I hope this helps.
Solve for c.
c= -9 - 8c
Answers
c=-9-8c
+8c
9c=-9
c=-1
Hope this helps:D!!
The letter C is equal to negative one.
c = -1
Hope this helps!
A certain class has 25 students. If 8 students play football and, 10 plays baseball and 6 plays both, how many students play neither football nor baseball?
Answers
Answer:1
Step-by-step explanation:
8+10=18 18+6=24 25-24=1
Answer:
7
Step-by-step explanation:
8 fb
10 bb
6 both, but are among the 8 & 10
so 7
hope it helps
You have a jar of jolly ranchers that contains: 15 cherry, 10 blue raspberries, 6 green apples, and 4 grapes.
Without looking, what is the probability that you select a green apple jolly rancher, eat it, then select a cherry?
The probability that both events occur is
which is
%. Round percent to the nearest whole
number.
Done and Review
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INTI
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Answers
Answer:
9 / 119 or 8%
Step-by-step explanation:
there are a total of 35 candies, of which 6 are green and 15 are cherry
P(Green) = 6/35
P(Cherry) = 15/35
P(Green,Cherry) = 6/35 · 15/34
= 9/119 or 7.6%
james has a rope that is 7 1/2 meters in length. He must cut the rope into 1/2 meter strips for a home improvement project he is working on. How many 1/2 meter strips can he cut?
Answers
Answer:
He can cut 15 1/2 meter strips.
Step-by-step explanation:
10 1/2 meter strips are 5 meters in length.
5 1/2 meter strips are 2.5 meters in length.
5 + 2.5 = 7.5 meters in length
find the solution to the system of equations
-9x+8y=-26
-9x-6y=-12
first answer gets brainliest! :)
Answers
Answer: y=-1 and x=2
Step-by-step explanation:
-9x+8y=-26
-9x-6y=-12
Subtract
14y = -14
Divide by 14
Y=-1
Substitute y=-1 into the equation
-9x-6(-1)=-12
-9x+6=-12
Subtract 6
-9x=-18
Divide by -9
X=2
what is twin prime ?
Answers
Answer:
A twin prime is a prime number that is either 2 less or 2 more than another prime number
is 540 or 630 closest to 594
Answers
Answer:
630
Step-by-step explanation:
630 - 594 = 36
594 - 540 = 54
630 is closest to 594
Answer:
630 is closer
Step-by-step explanation:
The number of units separating 540 and 594 is 54; that separating 594 and 630 is 36. So 630 is closer to 594.
If Vincent travels 96 miles in 1.5 hours. What is
his rate of speed?
Answers
Answer:
64 Miles per hour
Step-by-step explanation:
hope this helps!
If I need 2 teaspoons of oil for every 4 cups of flour to make 1 batch of
chocolate chip cookies, what would be the ratio I need to make 2 batches
of cookies. How many teaspoons of oil to how many cups of flour?
Answers
Answer:
2:4 or simplify and get 1:2
Step-by-step explanation:
2 tsp. of oil every 4 cups of flour.
If I saved 100 dollars every week from now until June how much money will I have ?
Answers
Answer:
2800 dollars probably because it's about 28 weeks and 2 days from now to June so if you multiply 100 by 28 the answer is 2800$
Answer:
Now we're the 14th of Nov 2021. The first week of June 2022 is in 28 week from now, so it's 100 dollars x 28 weeks = 2800 dollars
Geometry- Copy and complete the statement.
Answers
Answer:
X+y over y
Step-by-step explanation:
X+y over y
Hope it helps
7/3, 8/9, 12/5 order from smallest. please explain me 8/9 as its very confusing. i will give points and brainliest answer to nicly explained answer.
Answers
Answer:
8/9,7/3,12/5
Step-by-step explanation:
8/9 is smallest because the the numerator(upper number)is smaller than the denominator (which is the bottom number)so the value will be smaller than 1 unlike the other two fractions their numerator is bigger than the denominator so the value of them will be bigger than one