The following is the recursive formula for the arithmetic sequence in this issue:
c(1) = -16.
c(n) = c(n - 1) - 17.
An arithmetic sequence is a series of numbers where each term is obtained by adding a fixed constant, known as the common difference, to the previous term. For example, in the sequence 2, 5, 8, 11, 14, 17, each term is obtained by adding 3 to the previous term.
The formula for finding the nth term of an arithmetic sequence is: a(n) = a(1) + (n-1)d, where a(1) is the first term, d is the common difference, and n is the term number. For example, to find the 10th term of the sequence 2, 5, 8, 11, 14, 17, we would use the formula a(10) = 2 + (10-1)3 = 29. Arithmetic sequences have many practical applications, such as in finance, where they can be used to calculate the interest earned on an investment over time.
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If the sum of three consecutive natural numbers is 30 , find the numbers. Let us first form the equation. If y is the smallest among the three consecutive natural numbers, then the second smallest would be y+$ and the largest would be .
Answer: 9, 10, and 11
Step-by-step explanation:
If the sum of three consecutive natural numbers is 30, then we can represent the smallest of the three numbers as x. The next two consecutive natural numbers would be x+1 and x+2. Therefore, we can form the equation:
x + (x+1) + (x+2) = 30
Simplifying the left-hand side, we get:
3x + 3 = 30
Subtracting 3 from both sides, we get:
3x = 27
Dividing by 3, we get:
x = 9
Therefore, the three consecutive natural numbers are 9, 10, and 11.
Mrs Smith walks a half a mile a day after work. She works five days a week. How many yards will she have walked for the week by Friday morning?
The distance Mrs. Smith covers is 3520 yards during the duration of the week by Friday morning.
One week has seven days in total.
Mrs. Smith walks half a mile each day after work, she walks a total of
0.5 miles/ day × 7 days/ week = 3.5 miles/ week
Now, if we calculate the distance on Friday morning, she must have walked four times till Friday morning since she has to walk after her work.
Therefore,
0.5 miles/ day × 4 days = 2 miles
To convert miles to yards, we can use the fact that there are 1760 yards in one mile:
2 miles/week × 1760 yards/mile = 3520 yards/week
Therefore, by Friday morning, Mrs. Smith will have walked 3520 yards.
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Find dy/dx if y=u^3 + 2u and u= x^2 + 5
Answer: I hope this helped!
Step-by-step explanation:
.
What is a formula for the nth term of the given sequence? 24 , 36 , 54
The formula for the nth term of the series will be (11+n)*(n+1).
What is series?A series in mathematics is essentially the process of adding an infinite number of quantities, one after the other, to a specified starting quantity. A significant component of calculus and its extension, mathematical analysis, is the study of series. The fundamental concepts in mathematics are series and sequence. A series is the total of all elements, whereas a sequence is an ordered group of elements in which repeats of any kind are permitted. One of the typical instances of a series or a sequence is an arithmetic progression.
In this the pattern of the series is
24=12*2
39=13*3
54=14*4
hence The formula for the nth term of the series will be (11+n)*(n+1).
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Given the equation negative 24 equals y over 8, solve for y.
Answer: y = -192
Step-by-step explanation:
The equation given is:
-24 = y/8
To solve for y, we need to isolate the variable y on one side of the equation. We can do this by multiplying both sides by 8:
-24 x 8 = y
Simplifying the left side:
-192 = y
Therefore, the solution is y = -192.
1) Adam wants to buy a home priced at $215,000. The bank requires him to make a 5% down payment and
he will finance the rest for 30 years at 4.5% interest. He has to also pay the closing costs below. Find the
a) the down payment b) the amount of the mortgage c) the closing costs d) the amount financed with
closing costs e) the monthly payment f) the total amount repaid g) the amount paid to interest.
Application Fee
Borrower's Credit check
Points
Appraisal Fee
Title Search
Title Insurance
Attorney Fee
Documentation stamp
Processing fee
$ 25
65
1.5% of Mortgage
350
215
450
400
0.30% of Mortgage
1.25% of Mortgage
Landon buys cookies and lemons at the store he pays a total of $29.12 He pays $2.66 for the cookies he by seven bags of lemons that each cost the same amount Which tape diagram could be used to represent the contacts if X represents how much each bag of lemons cost
The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).
what is unitary method ?A way for resolving proportionality issues is the unitary method. Finding the value of one unit and then using that value to determine the value of another unit in relation to the first is what this process entails. If we already know that three pens cost $6, for instance, we can use the unitary technique to get the price of five pens as follows: 1 pen costs $6, 3 pens cost $2. Five pens cost $10, or $5 multiplied by $2.
given
The arrow on the right in the diagram above, which is equal to $29.12, represents the total cost of the cookies and lemons.
The first segment on the left, which is $2.66, represents the price of the cookies.
The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).
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Find a particular solution Find a particular solution to the differential equation dạy 4. dy +5 dt + 3y = edit dt2 In the form y = Aedit, where A is a complex constant. Here i = -1 is the square root of -1. g(t) = symbolic expression 2
A particular solution to the differential equation is [tex]y = Ae^(iwt) =(1/4)e^({i\sqrt{3t} )}.[/tex]
A particular solution to the differential equation,
[tex]\frac{d^4y}{dt^4} +5\frac{d^2y}{dy^2} +3y=2[/tex],
we assume that y has the form [tex]y = Ae^(iwt)[/tex], where A is a complex constant and w is a real constant to be determined. Substituting this form of y into the differential equation, we get:
[tex](-w^4 + 5w^2 + 3)Ae^(iwt) = 2.[/tex]
we solve the quadratic equation [tex]-w^4 + 5w^2 + 3 = 0[/tex], which can be factored as:
[tex](w^2 - 3)(-w^2 + 1) = 0.[/tex]
The roots are w = ±√3 and w = ±i. Since w must be real, we choose w = √3. Substituting this value of w and solving for A, we get:
[tex]A= \frac{2}{\sqrt{(-\sqrt{3} )^4 + 5(\sqrt{3})^2 +3 } }[/tex] [tex]=\frac{2}{5+3} = \frac{1}{4}[/tex]
Therefore, the particular solution is:
[tex]y = Ae^(iwt) =(1/4)e^({i\sqrt{3t} )}.[/tex]
A differential equation is a mathematical equation that relates a function to its derivatives. It is a powerful tool used in many fields of science and engineering to describe how physical systems change over time. The equation typically includes the independent variable (such as time) and one or more derivatives of the dependent variable (such as position, velocity, or temperature).
Differential equations can be classified based on their order, which refers to the highest derivative present in the equation, and their linearity, which determines whether the equation is a linear combination of the dependent variable and its derivatives. Solving a differential equation involves finding a function that satisfies the equation. This can be done analytically or numerically, depending on the complexity of the equation and the available tools.
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A bag of oranges weighs 1.5 kg to the nearest 100 g. Complete the error interval, where x is the weight of the oranges.
Construct triange ABC, in which AB = 6 cm, angle BAC = 96 degrees and angle ABC = 35 degrees. Measure the length of BC. Give your answer to 1 d. P
From the construction of the triangle ABC we get that the measure length of BC is approximately 4.22cm
To construct triangle ABC, we can follow these steps:
Draw a line segment AB of length 6 cm.Draw an angle of 96 degrees at point A using a protractor.Draw an angle of 35 degrees at point B using a protractor.The intersection point of the two lines that were drawn in step 2 and 3 will be point C, which is the third vertex of the triangle.To measure the length of BC in triangle ABC, we can use the law of sines.
The law of sines states that in any triangle ABC:
a / sin(A) = b / sin(B) = c / sin(C)
Where a, b, and c are the lengths of the sides of the triangle opposite to the angles A, B, and C, respectively.
In our triangle ABC, we know AB = 6 cm, angle BAC = 96 degrees and angle ABC = 35 degrees. We can find the measure of angle ACB by using the fact that the sum of the angles in a triangle is 180 degrees:
angle ACB = 180 - angle BAC - angle ABC
= 180 - 96 - 35 = 49 degrees
Now, we can apply the law of sines to find the length of BC:
BC / sin(35) = 6 / sin(96)
BC = 6 × sin(35) / sin(96)
Using a calculator, we can evaluate this expression to get:
BC ≈ 4.22 cm
Therefore, the length of BC in triangle ABC is approximately 4.22 cm.
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NEED HELP PLEASE HELP
Answer: Its Slope
Step-by-step explanation: in the given graph both lines a parallel .meaning they both should have the same slope
The following question has two parts. First, answer part A. Then, answer part B.
A fortune cookie has these dimensions.
A purple rectangle is shown. Its height is labeled as five-eighths, and its length is labeled as 2 and one-half.
Part A
Jonathan says he knows that
1
2
of
2
1
2
is
1
1
4
. And he knows that
5
8
is almost one half if you use estimation. But he is not sure whether
5
8
×
2
1
2
will be more or less than
1
1
4
.
Select the correct option.
A.
5
8
×
2
1
2
is equal to
1
1
4
B.
5
8
×
2
1
2
is less than
1
1
4
C.
5
8
×
2
1
2
is more than
1
1
4
D.
It is not possible to say using estimation.
Part B
Calculate the area of the fortune cookie.
A.
1
5
8
square inches
B.
1
25
16
square inches
C.
1
9
16
square inches
D.
1
25
16
square inches
1) 5/8 × 2 1/2 is slightly more than 1/4. Therefore, the correct option is:
C.
2) The area of the fortune cookie is: B. 1 25/16 square inches.
What is area?In mathematics, area is the measure of the size or extent of a two-dimensional shape or surface, such as a rectangle, triangle, circle, or any other closed figure. It is the amount of space inside the boundary of a shape, usually measured in square units.
For example, the area of a rectangle can be found by multiplying its length and width. The formula is:
Area = length × width
The area of a circle can be found by multiplying the square of its radius by pi (π). The formula is:
Area = πr²
where r is the radius of the circle.
Part A:
To estimate whether 5/8 × 2 1/2 is more or less than 1/4, we can round 5/8 to 1/2 and round 2 1/2 to 2. Then we have:
1/2 × 2 = 1
So, 5/8 × 2 1/2 is slightly more than 1/4. Therefore, the correct option is:
C. 5/8 × 2 1/2 is more than 1/4.
Part B:
The area of the fortune cookie can be found by multiplying its length by its height. The length is given as 2 1/2, which can be written as an improper fraction:
2 1/2 = 5/2
The height is given as 5/8. So, the area can be devised as:
Area = length × height
Area = (5/2) × (5/8)
Area = 25/16
Therefore, the area of the fortune cookie is:
B. 1 25/16 square inches.
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Which of the expressions below are equal to 8? Select all that apply. A) 2 + 2 + 2 + 2 B) 4 x 2 C) 1 x 8 D) 8 + 8 E) 4 + 4 + 4 + 4
Answer:
A ,B ,C
Step-by-step explanation:
2+2+2+2 equals 8
4x2 equals 8 and
1x8 equals 8
Answer:
A) 2 + 2 + 2 + 2
B) 4 × 2
C) 1 × 8
Hope this helps!
Step-by-step explanation:
A = 4 + 4 = 8
B = 8
C = 8
D = 16
E = 16
Amir drove from Jerusalem to the lowest place on Earth, the Dead Sea.
His altitude relative to sea level (in meters) as a function of time (in minutes) is graphed.
How long did it take Amir to reach sea level?
In order to solve this problem, we need to begin by examining the graph of Amir's altitude relative to sea level. We can see that the graph starts at an altitude of 700 meters and ends at an altitude of 400 meters.
We can also see that the slope of the graph is negative, which means that the altitude is decreasing over time. This means that it will take Amir some amount of time to reach sea level (which is 0 meters).
To calculate how long it took Amir to reach sea level, we can use the following equation:
Time = (Altitude Final - Altitude Initial) / (Rate of Change)
In this equation, the Rate of Change is the slope of the graph, which can be determined by examining the graph.
Plugging in our values, we get:
Time = (400 - 700) / (-6) = 100 / (-6) = -16.67 minutes
Therefore, it took Amir 16.67 minutes to reach sea level.
Brian can paint a room in 3 hours. Latoya can paint the same room in 2 hours and 15 minutes. How long would it take them if they worked together.
Answer: 45min
Step-by-step explanation:
3x60=180
2x60=120
120+15=135min
180-135=45min
The ratio of shirts to pants is 3 to 2. If there are 6 shirts, how many pants are there?
12
6
4
9
in 2015,the annual rate of population growth in the us was about 1.2%.find the growth factor forthe us
The annual rate of population growth in the US was about 1.2% in 2015, then the growth factor will be 1.012. The growth factor depends upon annual growth rate.
What is the growth factor?Growth factor typically refers to a constant multiplier that is used to calculate the growth or decay of a quantity over time. It is given as:
Growth factor = (1 + annual growth rate)
Therefore, the growth factor for the US in 2015 can be calculated as follows:
Growth factor (1+0.012) = 1.012
Therefore, the growth factor for the population of the US in the year 2015 was about 1.012.
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3. Find the distance from A to B. A(-2,2) B (4,-2)
The distance from points A(-2, 2) to B (4, -2) is equal to √52 units.
How to calculate the distance between the two points?Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical expression:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represents the data points (coordinates) on a cartesian coordinate.
Substituting the given points into the distance formula, we have the following;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(4 - (-2))² + (-2 - 2)²]
Distance = √[(6)² + (-4)²]
Distance = √(36 + 16)
Distance = √52 units.
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HELP PLEASE!!!! WILL MARK BRANLIEST
Answer:
To sketch the given region on the Argand diagram, we need to find the intersection of the three conditions:
-3i < Im(z) < 3i (the imaginary part of z lies between -3 and 3 on the vertical axis)
1 < Re(z) ≤ 6 (the real part of z lies between 1 and 6 on the horizontal axis)
|z - 4| ≥ 1 (the distance between z and 4 is greater than or equal to 1, which means z is outside or on the boundary of the circle centered at 4 with radius 1)
The first two conditions define a rectangle in the complex plane with vertices at (1,-3i), (1,3i), (6,3i), and (6,-3i). The third condition excludes the inside of a circle centered at 4 with radius 1, which means the region we want is the rectangle with a circular hole in the middle.
To find the area of this region, we can subtract the area of the circle from the area of the rectangle. The area of the rectangle is:
A_rect = length x width = (6 - 1) x (3i - (-3i)) = 30i
The area of the circle is:
A_circle = πr^2 = π(1)^2 = π
Therefore, the area of the region is:
A_region = A_rect - A_circle = 30i - π
So the area of the region is 30i - π, written in terms of π.
HELP ILL GIVE BRAINLY THINGY AND 100 POINTS
Answer is X=2.
1. Collect like terms
(x) + 4 + 9 = 17 - x
2. Add the numbers
x + (13) = 17 - x
3. Move the variable to the left-hand side and change its sign
x + 13 (+x) = 17
Move the constant to the right-hand side and change its sign
x + x = 17 - 13
4. Collect like terms
2x = 17 - 13
Subtract the numbers
2x = 4
5. Divide both sides of the equation by 2
Therefore, you get your solution: X=2.
Using the properties of equality, the steps for solving the equation is explained below.
How to Solve an Equation Using the Properties of Equalities?To solve an equation, we would apply the properties of equalities where necessary to isolate the variable in the equation to one side.
Step 1: [tex]3x + 4 - 2x + 9 = 17 - x[/tex] [given]
Step 2: [tex]x + 13 = 17 - x[/tex] [Combine like terms]
Step 3: Add x to both sides of the equation
[tex]x + 13 + x = 17 - x + x[/tex] [addition property of equality]
Step 4: [tex]2x + 13 = 17[/tex] [simplify]
Step 5: Subtract 13 from both sides
[tex]2x + 13 - 13 = 17 - 13[/tex] [subtraction property of equality]
Step 6: [tex]2x = 4[/tex] [simplify]
Step 7: [tex]x = 2[/tex] [division property of equality]
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if a watch costs $40 and you must pay 6.5% sales tax how much will the tax be ?
Answer:$2.60
Step-by-step explanation:40*0.065
Answer:42.06
Step-by-step explanation:
A person buys a bike for $360. He pays 60% of the cost price and then pays $15 over a period of 12 months. How much did he pay in total?
Answer: The person paid $396.
Step-by-step explanation:
1. Since we need to find 60% of 360, we can do 360 x 60/100.
2. We are now left with 216.
3. Now we have to add the total together.
4. 216 + (15x12) = 396.
5. The person paid $396.
please help i have been trying to get an answer for 5+ hours
How is the quotient of 556 and 16 determined using an area model?
Enter your answers in the boxes to complete the equations. Your final answer should be a mixed number in simplest form.
Answer:
To use an area model to determine the quotient of 556 and 16, we can divide a rectangle of area 556 into 16 equal parts. Each part will have an area of 556/16.
We can start by dividing 556 into 16 groups of 10 (160), and then into 16 groups of 3 (48). That leaves us with a remainder of 4.
So we have:
556 = 16 x 34 + 48 + 4
This shows that 556 can be written as 16 times some whole number (34) plus a remainder of 48 + 4/16.
Simplifying the remainder, we have:
48 + 4/16 = 48 + 1/4 = 48.25
Therefore, the quotient of 556 and 16 is:
556/16 = 34 1/4
The quotient of 556 and 16 using an area model can be determined by producing a rectangle with the total area of 556 and one side of 16. The length of the other side will be the quotient. In this case, the quotient is 34 3/4.
Explanation:When asked to determine the quotient of 556 and 16 using the area model, one way to think of this is making a rectangle. The total area is 556 and one side is 16. The length of the other side will be the quotient.
Start by first estimating how many times 16 could fit into 556. Let's take 30 as an estimate, because 30*16 = 480, which is relatively close to 556. Draw a rectangle with the width of 16 and the length of 30.
Find the difference between the rectangle's area and 556. So, 556 - 480 = 76. Now, 76 is our remaining area to fill. 16 goes into 76 four more times, adding up to 64.
There is still a leftover area, which is 76-64 = 12. This is smaller than our width of 16. So, your final answer is 34 12/16 or 34 3/4 in simplest form.
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To compare the pain control offered by two different analgesics in pediatric patients, the authors selected the Wong-Baker FACES pain rating scale as the primary end point. Before beginning the clinical trial, the authors sought to validate this ordinal scale by showing a correlation with a previously validated visual analog scale. Which one of the following statistical test is most appropriate to assess whether a correlation exists between these two measurements?
A. Pearson correlation
B. Analysis of variance (ANOVA)
C. Spearman rank correlation
D. Regression analysis
The most appropriate statistical test to assess whether a correlation exists between the Wong-Baker FACES pain rating scale and a previously validated visual analog scale is the (C) Spearman rank correlation.
What is correlation?Correlation refers to the connection between two variables in which a modification in one variable is linked to a modification in the other variable. Correlation can be positive or negative.
Spearman rank correlation- A non-parametric approach to test the statistical correlation between two variables is Spearman rank correlation, also known as Spearman's rho or Spearman's rank correlation coefficient. This is based on the ranks of the values rather than the values themselves. The results are denoted by the letter "r".
The formula for Spearman's rank correlation coefficient:
Rs = 1 - {6Σd₂}/{n(n₂-1)}
Where, Σd₂ = the sum of the squared differences between ranks.
n = sample size
Thus, the most appropriate statistical test to assess whether a correlation exists between these two measurements is the (C) Spearman rank correlation.
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Which equations arise when the steps of the Euclidean algorithm are reversed to express the greatest common divisor of each of these pairs of integers as a linear combination of these integers? (123, 2347) (Check all that apply.) Check All That Apply 1 = 10 - 3.3 1 = 37.10 - 3. 123 1 = 37.2347-706 - 123 1 = 37.10 -9.41 d d 1 = 36.2347-583 123
The equations that arise when the steps of the Euclidean algorithm are reversed to express the greatest common divisor of each of these pairs of integers as a linear combination of these integers are:
1 = 10 - 3.3, 1 = 37.10 - 3.123, and 1 = 37.2347-706 - 123.
What is the Euclidean algorithm?The Euclidean algorithm is a recursive method for finding the greatest common divisor (GCD) of two positive integers. When we divide the larger number by the smaller number, we obtain the remainder. The smaller number and the remainder are then passed on as input to the next round. The process continues until the remainder is zero, at which point the GCD is obtained.
The solution to the given problem is as follows:
We will use the Euclidean algorithm to compute gcd(123, 2347).
123 ÷ 2347 = 0 remainder 123.2347 ÷ 123 = 19 remainder 106.123 ÷ 106 = 1 remainder 17.106 ÷ 17 = 6 remainder 4.17 ÷ 4 = 4 remainder 1.4 ÷ 1 = 4 remainder 0.The last nonzero remainder we get is 1.
Therefore, the greatest common divisor (GCD)(123, 2347) = 1.
The greatest common divisor of 123 and 2347 can be expressed as a linear combination of the two numbers in the following ways:1 = 10 - 3.3, 1 = 37.10 - 3.123, and 1 = 37.2347-706 - 123.
Thus, the equations arising when the steps of the Euclidean algorithm are reversed to express the greatest common divisor of each of these pairs of integers as a linear combination of these integers are:
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I travel 480 km in 4 hours what is my speed in km/h
Answer:
120 km/h.
Step-by-step explanation:
480 km / 4h
Divide top and bottom by 4 to get the desired km/h.
We have 120 km/h.
Hope this helps!
Determine whether each of the following conditional statements is true or false. (a) If 10<7,10<7, then 3=43=4. (c) If 10<7,10<7, then 3+5=83+5=8. (b) If 7<10,7<10, then 3=43=4. (d) I…Determine whether each of the following conditional statements is true or false.(a) If 10<7,10<7, then 3=43=4.(c) If 10<7,10<7, then 3+5=83+5=8.(b) If 7<10,7<10, then 3=43=4.(d) If 7<10,7<10, then 3+5=83+5=8.
The given conditional statements are false, true, false, True.
They are determined by following:
(a) False - The statement "If 10<7,10<7, then 3=43=4" is false, since 10 is not less than 7.
(b) True - The statement "If 7<10,7<10, then 3=43=4" is true, since 7 is less than 10.
(c) False - The statement "If 10<7,10<7, then 3+5=83+5=8" is false, since 10 is not less than 7.
(d) True - The statement "If 7<10,7<10, then 3+5=83+5=8" is true, since 7 is less than 10.
Conditional statements are used in mathematics and logic to express relationships between events and conditions. These statements consist of an "if-then" structure, where the "if" clause is the antecedent or condition, and the "then" clause is the consequent or outcome.
The truth value of the conditional statement depends on whether the condition is true or false. If the condition is true, then the outcome is also true, and the statement is considered true.
If the condition is false, then the outcome may be true or false, and the statement is considered false. Conditional statements are widely used in mathematical proofs, programming, and reasoning to establish logical connections between different events and conditions.
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Simplify the expression.
n+ 3(n − 1) =
Solve, give all possible values of x
|2x+3| = 2
Answer:
-½ and -⁵/₂
Step-by-step explanation:
solve for both 2x +3 = 2 and 2x +3 = -2
An electronics company currently has 278 stores throughout the U. S. Because of the popularity of online shopping, many of the company's stores are closing. The total number of stores is expected to decline by about 5% this year. Assuming the same decline continues, you can use a function to approximate the total number of stores remaining after x years
We can estimate that after 5 years, there will be approximately 215 stores remaining.
Assuming a 5% decline in the number of stores each year, the function to approximate the total number of stores remaining after x years is exponential, and can be written in the form:
g(x) = a *[tex](0.95)^x[/tex]
where g(x) is the total number of stores remaining after x years, and a is the initial number of stores (278 in this case).
Therefore, the equation for the function is:
g(x) = 278 * [tex](0.95)^x[/tex]
This function takes into account the compounding effect of the 5% decline each year on the initial number of stores and can be used to estimate the number of stores that will remain after any number of years. For example, after 5 years, the number of stores would be approximate:
g(5) = 278 *[tex](0.95)^5[/tex]
g(5) ≈ 214.5
Therefore, we can estimate that after 5 years, there will be approximately 215 stores remaining.
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Complete Question:
An electronics company currently has 278 stores throughout the U.S. Because of the popularity of online shopping, many of the company's stores are closing. The total number of stores is expected to decline by about 5% this year. Assuming the same decline continues, you can use a function to approximate the total number of stores remaining after x years. Write an equation for the function. If it is linear, write it in the form gx=mx+b . If it is exponential, write it in the form gx=abx. gx=___?