The amount of money in a savings account increases by 0.2% every month.
Part A
Write a function for the amount of money in the account, B, after t months with an initial deposit of $100.
B(t) =
(
)t
Part B
By what factor does the amount in the account increase every month? Every year? Every 5 years? Round answers to the nearest thousandth.
each month:
each year:
every five years:
Answers
a) A function for the amount of money in the account, B, after t months with an initial deposit of $100 isB(t) = [tex]100(1 + 0.002)^t[/tex]
b) The amount in the account increases by a factor of approximately 1.002 every month, approximately 1.025 every year and approximately 1.099 every five years.
a) The function for the amount of money in the account after t months with an initial deposit of $100 and an increase of 0.2% per month can be written as:
B(t) = [tex]100(1 + 0.002)^t[/tex]
where t is the number of months.
b) To determine the factor by which the amount in the account increases every month, year, and five years, we can calculate the value of the function for t = 1, t = 12, and t = 60, respectively, and then divide each value by the previous one.
For each month:
B(1) = 100(1 + 0.002) = $100.20
B(2) = 100(1 + 0.002)² = $100.40
B(2)/B(1) = $100.40/$100.20 = 1.001993
The amount in the account increases by a factor of approximately 1.002 every month.
For each year:
B(12) = 100(1 + 0.002)¹² = $102.44
B(24) = 100(1 + 0.002)²⁴ = $105.01
B(24)/B(12) = $105.01/$102.44 = 1.0249
The amount in the account increases by a factor of approximately 1.025 every year.
For every five years:
B(60) = 100(1 + 0.002)⁶⁰ = $110.41
B(120) = 100(1 + 0.002)¹²⁰ = $121.20
B(120)/B(60) = $121.20/$110.41 = 1.0991
The amount in the account increases by a factor of approximately 1.099 every five years. Therefore, the amount in the account increases by a small factor every month, a moderate factor every year, and a larger factor every five years.
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Related Questions
Add: -8x8 + (-3x8 + 3)
Enter the correct answer.
Answers
1. Which of the following is a set or not?
(a) A=Set of tall man
(b) B=Set of beautiful women
(c) C=Set of tall students of class 10
(d) D=Set of counting number
(e) E=Set of good students
(f) F=Set of yellow roses
Answers
Step-by-step explanation:
Set of tall students of class 10 is a set. Thus, option C is the correct answer.
A set is defined as objects or things that can be justified as similar things combined together and grouped together.
The other sets are not specified. When we look at option A it is said that all the men are tall so they have a common factor i.e. they are tall but could have been more specified. Also in option B it is said that all the women are beautiful, here the common factor is beautiful but it could have been more specified. Similarly option d, option e and option f are also not specified.
When we look at option c, here it specified that the tal students are of class 10 and so I consider option "c" is the correct answer.
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3. Abby has 3 bags of oranges with 14,
23 and 28 oranges in them. Abby
rounds the number of oranges in each
bag to the nearest ten. About how
many oranges does Abby have
altogether?
Answers
Answer:
60
Step-by-step explanation:
14 rounds to 10
23 rounds to 20
28 rounds to 30
10+20+30=60
bao mom is picking him up from the ice rink she is at home which is located at the origin (0,0) how many total units is the ice rink away from the origin explain
Answers
The total units of length for the ice rink away from the origin is 14.42 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
Note: Ice rink is located at point (12, 8).
By substituting the given end points into the distance formula, we have the following;
Distance = √[(12 - 0)² + (8 - 0)²]
Distance = √[(12)² + (8)²]
Distance = √[144 + 64]
Distance = √208
Distance = 14.42 units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
prove that:
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)
Answers
The given identity (P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1) is proven below
How to prove the given identityGiven the following equation
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)
We start by simplifying the left-hand side of the equation:
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)= [(P²+1)/(P(P-1))] + [(P²+1)/(P(P+1))] - [(P²-1)/((P+2)P)] - [(P²+1)/((P-2)P)]
Next, we have the following steps to simplify the expression
= [(P³ + P² + P + 1)/(P(P²-1))] - [(P³ - 3P)/(P(P²-4))]
= [(P³ + P² + P + 1)(P²-4) - (P³ - 3P)(P²-1)]/[(P(P²-1))(P(P²-4))]
= [(P⁵ - 3P³ + P³ - 3P² + P² - 4P + P² - 4P - 4 + P³ - 3P)/(P⁴ - 5P² + 4)]
= [P⁵ - 2P³ - 6P² - 8P - 4]/[(P²-4)(P²-1)]
= -4(2p² + 1)/(p²-4) (p² - 1)
Hence, the given identity is proven.
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PLEASE HELP WILL MARK BRAINLY What is the area of a regular pentagon with a side of 5 ? Round the answer to the nearest tenth. TYPE THE NUMBER ONLY
Answers
Hope this helps.
write two different equations with variables and draw a diagram to solve the situation. For cleaning the attic Kristin was given $18. now she has $50. how much money did she have before
Answers
Once again, we get the same answer: Kristin had $32 before receiving the $18 for cleaning the attic. we solve this by forming equation and solving it
what is equation ?
An equation is a mathematical statement that shows that two expressions are equal. It usually consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems in various fields, including mathematics, physics, engineering
In the given question,
Let's use "x" to represent the amount of money Kristin had before receiving the $18 for cleaning the attic. We can set up the following equation:
x + 18 = 50
This equation represents the total amount of money Kristin has now, which is $50, after receiving the $18 for cleaning the attic. To solve for "x", we can subtract 18 from both sides of the equation:
x + 18 - 18 = 50 - 18
x = 32
Therefore, Kristin had $32 before receiving the $18 for cleaning the attic.
Alternatively, we can also use a diagram to represent the situation. We can draw a rectangle to represent the total amount of money Kristin has now, which is $50. We can then divide the rectangle into two parts: one part representing the $18 she received for cleaning the attic, and the other part representing the amount of money she had before. We can label this unknown amount as "x", and set up the following equation:
x + 18 = 50
This equation is the same as the one we set up earlier. To solve for "x", we can again subtract 18 from both sides of the equation:
x + 18 - 18 = 50 - 18
x = 32
Once again, we get the same answer: Kristin had $32 before receiving the $18 for cleaning the attic.
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using the table feature of a graphing utility what would be the intensity of an earthquake with an amplitude of 200,000 micrometers for 0.5 seconds?
Answers
Using the table feature of a graphing utility the intensity of an earthquake with an amplitude of 200,000 micrometers for 0.5 seconds would be 2.16 x 10¹⁴ joules/second/meter².
How did we get this ?First, note that the intensity of an earthquake with an amplitude of 200,000 micrometers for 0.5 seconds can be calculated using the formula..
I = (1/2)ρv²
Here I Intensity
ρ = density of the medium - this is a constatnt
v = velocity of the S-waves
If we used a graphing tool
a coumun ffor v will be created
a column for the formula for velocity will also be created.
The formula for velocity is
V = A/ T
A = amplitude
T = time or period in seconds
Since A = 200,000 micrometers; and
T = 0.05 secons
v = 200,000 / 0.5
v = 400,000 micrometer/sec
Back o the table, we ahve to add another oclumn for V²
then enter the values for V²
V² = 400,000²
v² = 160,000,000,000 micrometer²/sec²
Nowe we add another column which is
I = 1/2(pv²)
I = 2.16 x 10¹⁴ joules/second/meter².
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Sally is putting her dominions back into their storage tin. She wants to know how many dominoes can fit in the tin. While placing the dominoes in the tin, she counts how many dominos can be stacked on top of each other and she finds that to be 3 dominoes. She counts how many can be set side-by-side and she finds that to be 9 dominoes. Finally she counts how many can be placed end-to-end in the tin and she finds that to be 4 dominoes. Sally knows she can use addition to figure out how many total dominoes fit in the tin. She also knows that 27 dominoes fit in one row in the tin when she stacks up as many as she can in that row. Write an expression using only addition to show how Sally can determine how many dominoes can fit in the tin based on the number of dominoes in each row stacked
Answers
The expression that Sally can use to determine how many dominoes can fit in the tin based on the number of dominoes in each row stacked is (Number of rows stacked ÷ 0.75) x (9 x 4)
Sally can use the fact that she can fit 3 dominoes stacked on top of each other, 9 dominoes side-by-side, and 4 dominoes end-to-end in the tin to figure out how many dominoes can fit in the tin. Since she knows that 27 dominoes fit in one row stacked, she can use addition to determine the total number of dominoes that can fit in the tin.
First, she can find the number of dominoes that can fit in one layer of the tin by multiplying the number of dominoes that fit side-by-side and the number that fit end-to-end: 9 x 4 = 36.
Then, she can divide the total number of dominoes that fit in one row (27) by the number of dominoes that can fit in one layer (36): 27 ÷ 36 = 0.75.
This means that each layer of the tin can hold 0.75 rows of dominoes.
To find the total number of dominoes that can fit in the tin, Sally can multiply the number of layers by the number of dominoes in each layer: Number of layers x Number of dominoes in each layer = Total number of dominoes that can fit in the tin.
Therefore, the expression that Sally can use to determine how many dominoes can fit in the tin based on the number of dominoes in each row stacked is:
Total number of dominoes = Number of layers x Number of dominoes in each layer
Total number of dominoes = (Number of rows stacked ÷ 0.75) x (9 x 4)
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Evaluate each expression using the graphs of y=f(x) and y=g(x) shown below.
Answers
The composition of functions is solved and the expressions are
a) ( g o f ) ( -1 ) = 1
b) ( g o f ) ( 0 ) = 4
c) ( f o g ) ( -1 ) = -2
d) ( f o g ) ( 4 ) = -1
Given data ,
Let the composition of function be represented as A
Now , the value of A is
a)
( g o f ) ( -1 ) = g ( f ( -1 ) )
On simplifying the function , we get
when x = -1 , f ( -1 ) = 2
g ( 2 ) = 1
So , ( g o f ) ( -1 ) = 1
b)
( g o f ) ( 0 ) = g ( f ( 0 ) )
On simplifying the function , we get
when x = 0 , f ( 0 ) = 0
g ( 0 ) = 4
So , ( g o f ) ( 0 ) = 4
c)
( f o g ) ( -1 ) = f ( g ( -1 ) )
On simplifying the function , we get
when x = -1 , g ( -1 ) = 2
f ( 2 ) = -2
So , ( f o g ) ( -1 ) = -2
d)
( f o g ) ( 4 ) = f ( g ( 4 ) )
On simplifying the function , we get
when x = 4 , g ( 4 ) = 1
f ( 1 ) = -1
So , ( f o g ) ( 4 ) = -1
Hence , the composition of function is solved
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In this figure, ∠1 and ∠2 are located on a line.
Let m∠1=x° and m∠2=(4/5 x)°.
What is the value of x?
Answers
Answer:
x = 100
Step-by-step explanation:
1 and 2 are a linear pair and sum to 180° , that is
x + [tex]\frac{4}{5}[/tex] x = 180 ( multiply through by 5 to clear the fraction )
5x + 4x = 900
9x = 900 ( divide both sides by 9 )
x = 100
3. Arthur's mother is a mechanical engineer. She is designing
rectangular carts formoving finished goods from a factory's
manufacturing floor to the loading dock, where the goods are placed
on trucks.
She made a drawing showing where the carts must turn from a
hallway 48 inches wide to pass through a doorway 36 inches wide.
The drawing shows the longest cart that will pass through the
doorway.
to manufacturing floor 30 in.
G
E.
to loading dock
B
D
a) What kind of triangles are AABC and ACFD?
cart
36 in.
48 in.
b) In the drawing, one sixth of an inch represents 1 foot. What is the
scale factor of the drawing? Explain.
Answers
a) is Right angle Triangles both of them
b) The scale factor is 1:2.
How to solveGiven AFD = 90 degrees, So CFD = 90 degrees.
So it a Right Angle Triangle.
Again ABC = 90 degrees, It's also a Right Angle Triangle.
Here see both the Triangle are opposite to each other so according to the theorem sum of all three angles of a triangle is 180 degrees
so if any angle is 90 deg then the other two sum is also 90 deg.
Given the scale Factor, 1/6 inch = 1 foot,
So it is a Reducing Scale so let 'x' be in inches
So the Scale Factor = 1:2
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Please answer if you know this one with the steps thank you.
Answers
Answer: 36600 = E
Step-by-step explanation:
Given:
T=.2 (E - 10600)
T=5200
Find: E
Solution:
>substitute into thequation. You know T=5200
5200 = .2(E-10600) > Divide both sides by .2
26000 = E- 10600 > add 10600 to both sides
36600 = E
The two-way frequency table shows the results of a survey of students.
Right-handed
Left-handed
Total
In music program Not in music program Total
43
394
437
15
33
48
58
427
475
How many left-handed students are in the music program?
OA. 15
OB. 48
OC. 43
OD. 58
Answers
The left-handed students in the music program are option A 15 students.
What is two-way frequency table?A table that shows the frequencies of two category variables is known as a two-way frequency table. It is a method for succinctly and clearly organising and displaying data for two variables. One variable is represented by the table's rows, while the other variable is represented by the table's columns. The frequency of each combination of categories is displayed in the table's cells. To examine the relationship between the two variables and to spot patterns and trends in the data, a two-way frequency table can be employed. To summarise and analyse data, it is frequently used in statistics, the social sciences, and other disciplines.
From the given table the number of students that are in music program and left handed is given by the intersection of the row and column of the two.
Thus, he left-handed students in the music program are 15.
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A triangular prism and it’s net are shown below. The top and the bottom of the prism are shaded. All lengths are in centimeters.)
Answers
The solution is: the area of the shaded base in square centimeters is:
B= 15 cm²
Here, we have,
The base of the triangular shaped wedge of cheese is a right-triangle.To find the area of a right-triangle you apply the formula for half base by height.
A=1/2*b*h
= base area
= B
In this case, assume the sides of the triangle given are;
a=5 cm and b=6 cm,
thus area will be 1/2*6*5 =15 cm²
Hence, the area of the shaded base in square centimeters is :
B= 15 cm²
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complete question:
Evelyn cut a wedge of cheese into the shape of a triangular prism-like the one shown below. The shaded part represents one of the bases of the prism.
A formula for the volume of a triangular prism is v=Bh . Which equation can be used to find B , the area of the shaded base in square centimeters?
A diamond ring was bought a number of years ago for R3 180,00. The value of the ring increases by 4% per year. Answer the following questions: a. Determine the exponential function that describes the value of the ring after t years. b. Determine the value of the ring nine years after it was bought Choose the correct answers. Select one: a. C. a. V(t) = 3 180,00(1,4)* b. a. V(t) = 3 180,00 × (1+0,04)* b. R4 352,04 d. a. V(t) = (3180,00 × 1,04)* b. R4 526,13 a. V(t) = 3 180,00 x 1,04 b. R4184,66 b. R4526,13
Answers
V(t) = 3 180,00 × (1+0,04)^t
b. To determine the value of the ring nine years after it was bought, we can substitute t = 9 into the exponential function:
V(9) = 3 180,00 × (1+0,04)^9
V(9) = 3 180,00 × 1,04^9
V(9) = R4 526,13
Therefore, the correct answer is b. R4 526,13.
Is this correct for problem 15?
Answers
The solution to the given inequality is: 10 > x ≤ 12
How to solve Inequality expressions?Inequalities are defined as mathematical expressions that involve the symbols >(greater than), <(less than), ≥(greater than or equal to) and ≤(less than or equal to).
In order for us to 'solve' an inequality, we have to find a range, or ranges, of values that an unknown x can take and still satisfy the inequality.
We are told that the angle (9x + 7)° is greater than 97° and at most 118°
Thus:
9x + 7 > 97
9x > 90
x > 10
Similarly:
9x + 7 ≤ 115
9x ≤ 108
x ≤ 12
Thus, the solution to the inequality is: 10 > x ≤ 12
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A car pulls the emergency hand brake, accelerating at -4.0 m/s2 for 7.5 seconds to a complete and total stop. What was the initial velocity of the car before the brake was pulled?
Answers
The initial velocity of the car before the brake was pulled is 30m/s
What was the initial velocity of the car before the brake was pulled?From the question, we have the following parameters that can be used in our computation:
A car pulls the emergency hand brake, accelerating at -4.0 m/s2 for 7.5 seconds
This means that
Acceleration = -4.0m/s^2
Time = 7.5 seconds
Using the above as a guide, we have the following:
Initial velocity = -Acceleration * Time
substitute the known values in the above equation, so, we have the following representation
Initial velocity = 4 * 7.5
Evaluate
Initial velocity = 30
Hence, the initial velocity is 30
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the length and width of a rectangular piece of paper were measured as 60cm and 12cm respectively, determine the relative error in the calculation of it's area.
Answers
Answer:
Step-by-step explanation:
actual area : 60 x 12 = 720
1/2 = 0.5
60 + 0.5 = 60.5 12 + 0.5 = 12.5 -max area = 60.5 x 12.5 = 756.25
60 - 0.5 = 59.5 12 - 0.5 = 11.5 -min area = 59.5 x 11.5 = 684.25
absolute error : 1/2(756.25-684.25) = 36
relative error : 36/720 = 0.05
... your welcome
At Wynne College, there are 240 students in Year 12.
The interquartile range of the times taken for these students to travel to college is 32 minutes.
How many of these students have travel times within this interquartile range?
Answers
About 120 students have travel times within the quoted interquartile range.
InterquartileThe interquartile range (IQR) represents the range of the middle 50% of a set of data, which is the difference between the third quartile (Q3) and the first quartile (Q1).
Assuming that the travel times are normally distributed and that we have information on the quartiles, we can use the formula:
IQR = Q3 - Q1
To find the number of students whose travel times fall within the interquartile range, we need to know the values of Q1 and Q3.
Since the IQR is 32 minutes:
32 = Q3 - Q1
We also know that the total number of students in Year 12 is 240. Assuming that all students have reported their travel times, we can use the interquartile range to estimate the proportion of students whose travel times fall within this range.
If the interquartile range covers the middle 50% of the data, then each quartile should cover 25% of the data. Therefore, we can estimate that the number of students whose travel times fall within the interquartile range is:
Number of students = 240 x 0.50 = 120
Therefore, we estimate that 120 of the 240 Year 12 students have travel times within the interquartile range of 32 minutes.
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Helpppppp pleaseeeee
Answers
The resulting matrix from an elementary row operation to get a 1, in row 1 column 1 is:
R₁ = [1 4 -8] and R₂ = [2 4 7]
What is the row of a matrixA rectangular array of numbers or mathematical objects which are arranged in rows and columns is called a matrix. Each row of a matrix is a horizontal sequence of numbers or objects that are separated by commas and enclosed within square brackets, and it represents a vector in the row space of the matrix.
The row operation R₁ - 4 — R₁ will be carried out as follows:
5 - 4 = 1 {row 1 column 1}
9 - 4 = 5 {row column 2}
-4 - 4 = -8 {row column 3}
Therefore, the resulting matrix from an elementary row operation to get a 1, in row 1 column 1 will have:
R₁ = [1 4 -8] and R₂ = [2 4 7]
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Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
Answers
Answer: X = 25
Step-by-step explanation: Since 36 divided by 2 equals 18, which would cancel out the two on the left side leaving us with. (x - 7) = 18 we can add 7 to both sides to get. X = 25
Edit: To whoever said my math is incorrect is wrong, I even double checked with multiple sources and people. It must’ve been a different equation or number. Sorry for not being able to help, however the math was correct.
Work out the value of fg^2 when:
f = -5 and g = -4
Answers
20^2 =400
ANSWER=400
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
The result of the logarithm function is equal to 9. (Correct choice: D)
How to determine the missing component in a logarithm
The statement shows an incomplete logarithm, whose result must be found by understing relationships between trascendent functions. Logarithm functions and exponential functions are related in the following way:
aᵇ = n ↔ ㏒ₐ n = b
Where:
a - Baseb - Exponentn - ResultIf we know that (base) a = 3 and (exponent) b = 2, then the value of the result (n) is now defined:
n = 9
3² = 9
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I need help pleaseee
Answers
The matrix formed by performing the row operation 4R₂ + R₃ — R₃ will result to R₁ = [-4 0 1 5], R₂ = [-6 5 -1 8], and R₃= [-33 24 -9 32]
What is a matrix row operationRow operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.
performing the row operation 4R₂ + R₃ — R₃, we have;
4(-6) + (-9) = -33 {row 3 column 1}
4(5) + 4 = 24 {row 3 column 2}
4(-1) + (-5) = -9 {row 3 column 3}
4(8) + 0 = 32 {row 3 column 4}
Therefore, the matrix formed by performing the row operation 4R₂ + R₃ — R₃ will give a new one with R₁ = [-4 0 1 5], R₂ = [-6 5 -1 8], and R₃= [-33 24 -9 32]
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Find sin (ñ/4). Round to 3 decimal places.
Answers
Answer:To find sin(π/4), we can use the fact that sin(π/4) = sin(45°). We also know that sin(45°) = 1/√2 or approximately 0.707 (rounded to 3 decimal places). Therefore, sin(π/4) is approximately equal to 0.707.
Step-by-step explanation:
Find the circumference and the area of a circle with radius 4 m.
Use the value 3.14 for , and do not round your answers. Be sure to include the correct units in your answers.
4m
Circumference:
Area:
Answers
Area: 50.2654824574
Explanation:
Circumference formula is C = 2 π r
Plug in r (raidus) with 4
2π4 = ^above
Area formula is πr^2
Plug in r (radius) with 4
π4^2 = above
What is the base pic attached below
Answers
Answer: 2.5
Step-by-step explanation:
the base is always positive, and it says f(x)= 1/2*5^x
1/2*5 is 2.5, so I think the base is 2.5
hope it helped:)
Find the surface area of the composite solid to the nearest hundredth.
3 ft.
4 ft
2 ft
The surface area is about
square feet.
Answers
snip, that's wrong nvm (not sure how to delete)
Express all real numbers greater than 5 in interval notation.
Answers
All real numbers greater than 5 can be expressed in interval notation as:
(5, ∞)
How to express all real numbers greater than 5 in interval notation?Interval notation is a way of representing an interval on a number line. Simply, it is a method of writing subsets of the real number line.
All real numbers greater than 5 can be expressed in interval notation as:
(5, ∞)
Where the round bracket "(" means 5 is not included in the interval, and the infinity symbol "∞" means the interval continues indefinitely to the right.
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