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
Geometry help me!
Extra points!
Answers
Answer:
71
Step-by-step explanation:
Will give brainliest!
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Answer:
[tex] \frac{1}{2} + \frac{5}{8} [/tex]
[tex] \frac{1 \times 4}{2 \times 4} + \frac{5}{8} [/tex]
[tex] \frac{4}{8} + \frac{5}{8} [/tex]
[tex] \frac{9}{8} [/tex]
[tex]1 \frac{1}{8} [/tex]
Answer:
all, but the bottom
Step-by-step explanation:
They all add up correctly but the one on the bottom makes no sense.---------------------------------------------------------------------------------------------------------------------------
Hey can you guys help me pls :))
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Answer:
-d-1<2. => -(-2)-1=1<2. the forth option is true
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.
5(6a +1) = 7(4x + 3) w/steps
Answers
Answer:
[tex]\frac{15a- 8}{14} = x[/tex]
Step-by-step explanation:
Step 1 - Divide both sides of the equation by 7:
[tex]5(6a + 1) = 7(4x + 3)\\[/tex]
[tex]\frac{5(6a + 1)}{7} = \frac{7(4x + 3)}{7} \\\\\frac{5(6a + 1)}{7} = 4x + 3[/tex]
Step 2 - Subtract 3 from both sides to isolate the 4x:
[tex]\frac{5(6a + 1)}{7} - 3 = 4x + 3 - 3\\\frac{5(6a + 1)}{7} - 3 = 4x[/tex]
Step 3 - Expand equation:
[tex]\frac{5(6a + 1)}{7} - 3 = 4x \\\\\frac{30a + 5}{7} - 3 = 4x[/tex]
Step 4 - Translate -3 into a fraction and add it:
[tex]\frac{30a + 5)}{7} - 3 = 4x\\\frac{30a + 5 + (7 * -3)}{7} = 4x\\\frac{30a + 5 + (-21)}{7} = 4x\\[/tex]
[tex]\frac{30a - 16}{7} = 4x[/tex]
Step 5 - Divide both sides of the equation by 4:
[tex]\frac{\frac{30a - 16}{7}}{4} = \frac{4x}{4}[/tex]
Multiply the two fractions together to simplify:
[tex]\frac{30a - 16}{4 * 7} = \frac{4x}{4}[/tex]
[tex]\frac{30a - 16}{28} = x[/tex]
Step 6 - Simplify by dividing the fraction by 2:
[tex]\frac{(30a \div 2)- ( 16 \div 2)}{28 \div 2} = x[/tex]
[tex]\frac{15a- 8}{14} = x[/tex]
Hope this helps!
Figure A
Figure B
Which of the triangles in the two figures above is a right triangle? Explain your choice using
the Pythagorean Theorem to prove it. Note: the figures are not drawn to seale.
Answers
Figure B
Step-by-step explanation:The Pythagorean Theorem is [tex]a^2 + b^2 = c^2[/tex], where c is the longest side of the triangle (the hypotenuse).
To find the side length of each square, you have to square root the area of each square. This means that Figure A has side lengths of 3, 6 and 8 units. Figure B has side lengths of 5, 12 and 13 units.
In Figure A, if the triangle is right-angled, the equation [tex]3^2 + 6^2 = 8^2[/tex] must be correct. 9 + 36 = 45. 45 is not equal to 64, so the triangle is not right-angled.
In Figure B, if the triangle is right-angled, the equation [tex]5^2 + 12 ^2 = 13^2[/tex] must be correct. 25 + 144 = 169. 169 is 13 squared, so the triangle is right-angled.
Alternatively, as you are already given the square values for each side length, there is no need to square root and square again. You can just test if the two smaller areas equal the larger area, but the explanation above uses a more detailed example of the Pythagorean Theorem.
In two or more complete sentences describe how to determine if the function, f(x) =3cos(x) is even by looking at a graph
Answers
Answer:
You know that a cosine graph is a sine graph moved to the left by pi/2, therefore, like a linear equation, you need to make the cosine graph 3 times less width.
Step-by-step explanation:
What is the area of this tile
Answers
Explanation: 4x1=4
Answer:
4in^2
Step-by-step explanation:
1x4=4 and then ^2 because it's square inches
Help please I really need it!!!
Answers
Answer:
They are similar
Step-by-step explanation:
If a triangle has the same two angle as another one it means that they are similar triangles. this is because all triangles have 180 degrees shared between all of the angles in them. that is the case for these triangles.
hope this helps!
I got the answer but I don't know how to show my work, can ya'll tell me what I should write??
Answers
Answer:
one side is 16, the other is 8[tex]\sqrt{3}[/tex]
Step-by-step explanation:
30-60-90 angle triangle always give the following sides
1-[tex]\sqrt{3}[/tex]-2 , which is a-b-c
to label your triangle as such
8= a
other leg =b
hypotenuse = c
so. if a =8, then
c = 8*2 =16
b=8[tex]\sqrt{3}[/tex]
If you the numbers 2 and 2, what will the final sum be
Answers
Singer A and Singer B had the two top-grossing concert tours for a certain year, together generating $334 million in ticket sales. If Singer B took in $26 million less than Singer A, how much did each tour generate?
Answers
Creflo is 6 years older than Dean.
Raheem is twice as old as Creflo.
The sum of their ages is 34.
Work out the ratio of Dean's age to Creflo's age to Raheem's age.
Answers
R = 2C
D + C + R = 34
R = 2 (D+6)
R = 2D + 12
D + (D + 6) + (2D + 12) = 34
Add like terms.
4D + 18 = 34
4D = 34 - 18
4D = 16
D = 4
C = D + 6
C = 4 + 6
C = 10
R = 2C
R = 2(10)
R = 20
Write as ratio.
D:C:R
4:10:20
Find the probability of flipping a coin 3 times and getting all heads.
Answers
Answer:
.13
Step-by-step explanation:
Write an expression to represent:
Nine less than the quotient of two and a number z.
Answers
Answer:
2 / z - 9
Step-by-step explanation:
Don't worry division always goes before subtraction so you don't need any parenthesis.
Tell me if I'm wrong :)
¿Cuál es la probabilidad de que una mujer que ha sido vacunada en este lapso de cuatro
meses haya recibido su segunda dosis en octubre ?
Answers
Answer: buddy if you put it in English i can do it I’m a teacher
Step-by-step explanation:
Of the students in your class, 12% are left-handed. What fraction of the students are left-handed? Are there more right-handed or left-handed students? Explain. Write your answers in simplest form. A comparison of these two fractions is:
Answers
Answer:
3/25
More right handed
3/25 ≤ 22/25
Step-by-step explanation:
There are more right handed people because 88% of them are right handed.
12/100 = 3/25
What is the answer
Answers
Answer:
It's a im taking the same test lol
Step-by-step explanation:
There are 18 girls and 12 boys on the swim team. What FRACTION of the team is made up of boys?
Answers
Answer:
12/30
Step-by-step explanation:
Hope this helps man. Have a GREAT day.
Sincerly, lipor
A 12/30 fraction of the team is made up of boys.
What is a fraction?A fraction is defined as part of a whole.
The total number of team members is
12+18=30
The number of boys on the team is 12.
Hence, the fraction of boys o the team is 12/30.
To learn more about fraction, use the link given below:
https://brainly.com/question/10354322
#SPJ2
Find the values of x and y.
Answers
Answer:
Y = 69
X = 42
Hope this helps!
I need help with this question! Whoever is correct, I will give brainliest!
Answers
The system of equations that can be used to model the situation is:
B. [tex]x + y = 27[/tex][tex]y = 3 + \frac{1}{2}x[/tex]What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: number of boxes Juan packed.Variable y: number of boxes David packed.Together they packed 27 boxes, hence:
[tex]x + y = 27[/tex]
David packed 3 more than half the number Juan packed, hence:
[tex]y = 3 + \frac{1}{2}x[/tex]
Hence, the system of equations that models the situation is:
B. [tex]x + y = 27[/tex][tex]y = 3 + \frac{1}{2}x[/tex]You can learn more about system of equations at https://brainly.com/question/25960609
. A coach divided his team into two proups of equal size. 5/8 of the first group drinks at least 2 glasses of water a day. 75% of the second group drinks at least 2 glasses of water a day. What fraction of the team drinks at least 2 glasses of water a day?
a 1/2
b 5/8
c 11/6
d 3/4
Answers
Answer:
b is the answer of the question because it is the only answer
find the measure of angle y, 38,41,19
Answers
12 people sharing an 8 gummy worm pieces how much per person will get equally show two ways
Answers
which is not a factor of 36
Answers
Answer:
all numbers to 36 except 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Step-by-step explanation:
PLS HELPPPP
Answer the following problem using the SOLVE Method
Math Club members are selling Math club members are selling Pi Day T-shirts for $7.50 each. The goal is to
raise $500 by Friday. The figure below shows how much they have raised by
Wednesday. What is the minimum number of T-shirts they must still sell in
order to reach their goal? Explain your reasoning.
Answers
The minimum number of T-shirt that they must sell to raise $500 is 67 T-shirts
Let x represent the number of Pi Day T-shirts sold.
They are selling Pi Day T-shirts for $7.50 each, So to raise $500:
7.5x > 500
Dividing through by 7.5:
7.5x / 7.5 > 500 / 7.5
x > 66.7
Hence, the minimum number of T-shirt that they must sell to raise $500 is 67 T-shirts
Find out more at: https://brainly.com/question/25285332
I think of a number. I add 3 then divide it by 2. My answer is 12. Form an equation and solve it to find my number.
Answers
Answer:
21
Step-by-step explanation:
21 plus 3 equals 24 divided by 2 equals 12
An investor invested a total of $3,000 in two mutual funds. One fund earned a 7% profit while the other earned a 3% profit. If the investor's total profit was $142, how much was invested in each mutual fund?
Answers
Answer:
Step-by-step explanation:
x= fund that got 7%
y= fund that got 3%
x+y=3000
.07x+.03y=142
y=3000-x
.07x+.03(3000-x)=142
.07x+90-.03x=142
.04x=52
x= 1300
x+y=3000
1300+y=3000
y=1700
1300 in the fund that earned 7%
1700 in the fund that earned 3%
need help with this math question
Answers
Answer:
please resend question
Step-by-step explanation:
solve pls brainliest
Answers
Answer:
16 sq mm
Step-by-step explanation:
hope this helps
Can u give me a brainliest answer?
Area of the figure= 2x2 + 2x6
Area of the figure= 4+12
Area of the figure = 16m^2