g An employee joined a company in 2017 with a starting salary of $50,000. Every year, the employee receives a raise of $1,000 plus 5% of the salary of the previous year. (a). Set up a recurrence relation for the salary of the emplyee n years after 2017. A recurrence relation of a sequence is an equation that express a subscript n using one or more of previous terms. (b). What will be the salary of the employee in 2025

Answers

Answer 1

Answer:

a) s[n] = 1.05s[n-1] +1000; s[0] = 50,000

 b) $83,421.88

 c) s[n] = 70000·1.05^n -20000

Step-by-step explanation:

a) Let s[n] represents the employee's salary in dollars n years after 2017. The salary in 2017 is given as $50,000, so ...

 s[0] = 50000 . . . . the recursion relation initial condition

The next year, the salary is multiplied by 1.05 and 1000 is added:

 s[1] = 1.05·s[0] +1000

This pattern repeats, so the recursion relation is ...

 s[n] = 1.05·s[n-1] +1000

__

c) It is convenient to find a formula for the salary before trying to compute the salary 8 years on. So, we work part (c) before part (b).

The base salary gets multiplied by 1.05 each year, so can be described by the exponential function ...

 base salary after n years = 50,000·1.05^n

The add-on to the raise becomes a geometric sequence whose common ratio is 1.05. The sum can be described by the formula for the sum of such a sequence:

 sum = a1(r^n -1)/(r -1) . . . . . (see note below)

 sum of add-ons = 1000(1.05^n -1)/(1.05 -1) = 20000(1.05^n -1)

So, the total salary after n years is ...

 s[n] = 50000·1.05^n + 20000(1.05^n -1)

The exponential terms can be combined, so we have the explicit formula ...

 s[n] = 70000·1.05^n -20000

__

b) The year 2025 is 8 years after 2017, so we want to find s[8].

 s[8] = 70000·1.05^8 -20000 = 70000·1.4774554 -20000

    = 103,421.88 -20000 = 83,421.88

In 2025, the employee's salary will be $83,421.88.

_____

Note on the sum of the add-ons

A geometric sequence starts with term a1 and gets multiplied by a ratio r to make the next term: a2=r·a1; a3=r²·a1, ....

The sum of such a geometric sequence has the formula

 Sn = a1·(r^n -1)/(r -1)

Here, the sequence starts in year 1 with a1=1000 and has a common ratio r=1.05. The denominator of the sum is r-1 = 0.05 = 1/20, so the sum can be written as

 Sn = 20000·(1.05^n -1).


Related Questions

Quickly answer number 10 text only no fonts (100 points) mark brainliest

Answers

25

have a great day! :3

Answer:

Hello again the square root of 625 is 25

A car is traveling at a steady speed. It travels 1 3/4 miles in 2 1/3 minutes. How far will it travel in 25 minutes? In 1 hour?

Answers

Answer: They would travel 17.25 miles in 23 minutes and 45 miles in 1 hour.

Step-by-step explanation:

If you divide 1 3/4 by 2 1/3 you get. 0.75 which is how far the car will travel each minute and then you can just multiply that number by however many minutes there are.

Find the next term in the geometric sequence that is calculated with a common ratio of 4 if the current term is 4

Answers

Answer:

16

Step-by-step explanation:

Multiply the term (4) by the common ratio (4)

4 * 4 = 16

You are shipping a box that weighs 13 pounds. Shipping charges are listed by ounces at the local mail center. How many ounces does the box weigh?

Answers

Answer:

208 ounces in 13 pounds

Step-by-step explanation:

Find the quotient or 4/5 and 6/7 give ur answer as a fraction in simplest form

Answers

Answer:

14/15

Step-by-step explanation:

Let me know if i got it right if not I'm sorry :(

The required quotient would be 14/ 15 which is a fraction.

What is the Quotient?

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

We have been given that two numbers are 4/5 and 6/7

To determine the quotient or 4/5 and 6/7

⇒ 4/5 ÷  6/7

⇒ 4/5 / 6/7

Reciprocal the term of denominator,

⇒ 4/5 × 7/6

Apply the multiplication operation,

⇒ 28 / 30

Reduce the above fraction to the simplest form

⇒ 14/ 15

Therefore, the required quotient would be 14/ 15 which is a fraction.

Learn more about the quotient here:

brainly.com/question/27796160

#SPJ2

true or false, when graphing a linear Inequality in two variables, the inequality symbol " < " states to use a broken line.

Answers

Answer:

Ture I tink

Step-by-step explanation:

Answer quickly! [tex]x^{2} = 6[/tex]

Answers

[tex]x = \pm \sqrt{6}[/tex]

katryn owes her father $25.write this number as an integer.

Answers

Answer:

-25

Step-by-step explanation:

When you owe someone something, in integers, your answer is in the negative.

Please help me figure this out.

Answers

the answer is akuma di ra your welcome

Estimate the difference by rounding each number to the nearest whole

367.2-294.8
A. 72
B.72.4
C.73
D.80

Answers

Answer:

A. 72

Step-by-step explanation:

367.2 -> 367

294.8 -> 295

367

- 295

____

072

if you weren't estimating you would get B because you wouldn't round the numbers.

since the question says to round and then estimate, the answer should be A.

Dilate the figure by the scale factor. Then enter
the new coordinates.
K = 2



Answers

Answer:

A = (-6, 4)

B = (2,2)

C =  (-2, 2)

Step-by-step explanation:

If a coordinate (x, y) is dilated by a factor of k, the resulting coordinate will be expressed as (kx, ky). Note that each coordinate is multiplied by the scale factor  Given the coordinates (-3,2),(1,1)(-1,-1), if they are dilated by a factor of 2, the resulting coordinate will be;

A = (2(-3), 2(2)) = (-6, 4)

B = (2(1),2(1)) =(2,2)

C = (2(-1), 2(-1)) = (-2, 2)

PLEASE, I need help ASAP !

Answers

Answer:

I'm not 100% sure but I think it's C.

it might also be B. it's one of those 2 for sure but I'm like %80 sure it’s C.

Step-by-step explanation:

please let me know if im right or wrong....

Help thank you so very much

Answers

X = 0

Hope it helps ya!

Answer:

x-0 12

Step-by-step explanation:

i hope cant help p please follow me in brainly and hearts and give me a star

Please help me I need help

Answers

When converted to a household measurement, 9 kilograms is approximately equal to a

CLASS 6 MATHS!!!! HELP ME PLEASE!!!!!!!​

Answers

Step-by-step explanation:

[tex] \\ 20. \: \: ( \frac{ - 3}{4} )(4\frac{1}{6} )[/tex]

[tex] \\ = \frac{ - 3}{4} \times \frac{25}{6} [/tex]

[tex] \\ = \frac{ - 25}{8} [/tex]

[tex] \\ = - 3.125[/tex]

[tex] \\ 21. \: \: ( - 3\frac{7}{8} )( - 5\frac{3}{4} )[/tex]

[tex] \\ = \frac{ - 31}{8} \times \frac{ - 23}{4} [/tex]

[tex] \\ = \frac{713}{32} [/tex]

[tex] \\ = 22.28125[/tex]

solve pls brainliest

Answers

Answer:

4.5341 < 6.9 < 6.906 < 6.96

Step-by-step explanation:

4.5341 is closer to 0 than 6.96 is.

Help me please i've been stuck on this question for hours.

Answers

Answer:

a) x^3 b) y^5

Step-by-step explanation:

you can combine the x's and y's to make a exponent equal to the number of x's or y's.

Homework help please

Answers

Answer:

h=-136

Step-by-step explanation:

..............

A photograph has a length that is 6 inches longer than its width, x. So its area is given by the expression x(x+6) square inches. If the area of the photograph is 112 square inches, what is the width of the photograph?

The width of the photograph is __inches.

Answers

Answer: 8 inches

Solving Steps:

x(x + 6) = 112
x^2 + 6x = 112
x^2 + 6x - 112 = 0
(x + 14)(x - 8) = 0
x + 14 = 0
x = -14
^^^ reject because distance can’t be negative
x - 8 = 0
x = 8

Check:

x(x + 6) = 112
8(8 + 6) = 112
64 + 48 = 112
112 = 112

Who can help me with this entire page?

Answers

Answer:

I'm not entirely sure what the question is but every thing under 12.5 is closer to 12, everything 12.5 and upwards like 12.87 would be closer to 13

HELPPPPPPPPPPPP PLEASEEEE

Answers

Answer:4

Step-by-step explanation:

Find the slope and y intercept of the line 3x+2y=-6

Answers

Answer:

Step-by-step explanation:

Slope -  -3/2

y-intercept- (0,-3)

Need help with math problem

Answers

Answer:

1/7

Step-by-step explanation:

Sana nakatutulong

#Carry on learning

Answer:

I Don't know if this is correct!

Step-by-step explanation:

1/7 of boys are not bringing their lunch as you can see.

I think it is 2/7

pls help i am in 8th grade k12
What is the equation of the line shown in this graph?

A function graph of a line with two points (-2,2) and (-2,-3) with an x axis of negative five to five and a y axis of negative five to five

Enter your answer in the box.

Answers

Answer:

x = -2

Step-by-step explanation:

Yeah if you have a new 7473

A city has a population of 280,000 people. Suppose that each year the population grows by 4.75% . What will the population be after 7 years ? Use the calculator provided and round your answer to the nearest whole number.

Answers

8.75% = 0.0875 P(t) = Initial Population * (1 + rate)t P(t) = 280,000(1 + 0.0875)t P(t) = 280,000(1.0875)t P(9) = 280,000(1.0875)9 P(9) = 595,692

What is the slope of 3x+4y=−2?

Answers

Answer:

subtract the 3x from one side and put in the other

4y = -3x -2

then divide both sides by 4

y= -3/4x -1/2

so the slope is-3/4

Point C is located at ( -6,5). Point D is located at (-2, y). The
* distance between points C and D is 5 units. Find a possible y
value for point D.
Select all possible answers.
Pick up to 0 answers.
А
1
B. 2
C. 5
D. 8
E 9

Answers

Answer:

Step-by-step explanation:

yes cdrj

ejkfkj

ennejw

Yen paid $10.50 for 2.5 pounds of pretzels. What price did she pay for each pound of pretzels?

After dividing 25 into 105, the next step is to
25 by 4.
The next step is to
100 from 105.
The next step is to
the next number.

Answers

The first step is to Multiply  The next step is to Divide.

Ok so if you were wondering what to do on the box that says this

Move Decimal

Divide

Multiply

Subtract

Bring down

On this, I agree with myself. The solution is straightforward. Simply click them in the sequence listed, beginning with the first and ending with the last. Wow, what sleuthing I did. I realize it's not much, but I was perplexed by this as well, so you could be as well. So here we go with the actual answer. To tackle these sorts of issues, you must employ a technique known as PEMDAS, which stands for.

Parenthisis

Exponent

Multiply

Divide

Add Subtract

I realize I spelt the first one incorrectly, but it's 2 a.m. and I'm doing homework for you. Now we must consider whether or not this has any parenthesis. This particular issue does not. Now we must determine whether or not this issue has exponents, which it does. As mentioned in the response box on the lesson's main page. So we have to consider that (spelled incorrectly, but who cares, it's math class)Now we multiply by a power of ten, so the divisor is a whole number. The following step is to divide by calculating how many times 25 equals 105. I realize it was stolen from the question, but whatever. So there was the explanation; I realize I didn't answer the entire problem, but I didn't have to; it wasn't in the cards.

Unit 3 parallel and perpendicular lines homework 2 please help quickly don’t understand front page

Answers

Answer:

this statement is confusing me

Step-by-step explanation:

cause I don't understand it

Karen is joining a book club. To join, she must buy two books, and then she will get one free book. The following are the prices for the 8 books being offered: A. $29.50 E. $16.25 B. $25.00 F. $19.98 C. $18.00 G. $49.00 D. $39.50 H. $17.98 Karen wants to select her books with the maximum dollar value and yet pay as little as possible. What three books should she select? A) A, C, D
B) A, B, G
C) C, E, H
D) E, G, H​

Answers

Answer:

the answer are is c,e,h because they have low prices

Other Questions
Los chicos no son Altos ,son use of chemical substance in our daily life their advantages and disadvantages 53.98% of the area under the distribution curve lies tothe left of it. Why was the Confederation shown to be a failure in the aftermath of the war?A. It could not print money to deal with its debt.B. It could not engage in foreign trade to increase the new country's profits.C. It needed all decisions to be made unanimously among all states.D. It could not collect taxes to deal with its debt.Submit (ii)Copper and potassium have different melting points and boiling points.Give one other difference between the properties of copper and potassium. Choose the appropriate response:Cuando eras nia, construamoscasas con tu hermano?A. No, ella no construa casas con tu hermano.B. Si, construa casas con tu hermano.C. S, yo construa casas con mi hermano. The Cortez family is traveling from Miami to Washington, D.C. They plan to average 55 miles per hour on their trip.About how many drive hours will it take the Cortez family to make the trip? 5) Add using Place-Value diagrams: 215 six + 43 six The circumference of a circle can be found using the formula c=2 pi r. Which is an equivalent equation solved for r 50 points! ! !Why did some counties in North Carolina secede to form their own governments? A) to avoid federal taxesB) to gain more control over their own rightsC) to protect their religious freedomD) to be able to own and farm their lands . There are 2 boys for every 3 girls in Mrs. Sorrentino's class. If there are 30 students inthe class, what percentage are boys?(Please show how to solve this question , step by step!) PLEASE HELP MEEEE THIS IS DUE IN TEN MINUTES ALSO HOW THE HECK DO YOU CHANGE THE THING THAT SAYS COLLEGE BY UR NAME? IM IN FLIPPING EIGTH GRADE NOT COLLEGE!!! What is procedural memory? tomaso is explaining to a colleague the different types dns attacks. which dns attack would only impact a single user? IF YOU ARE REALLY GOOD A MATH THEN PLEASE ANSWER THIS !!!Your help will be much appreciated because i am losing my sanity doing this math What is the slope of the line that contains these points Identify the factors of the terms of the expression.6 + 2a + 15b the factors of the terms are? 3x(6x + 5)4x(2x-3y) what is the answer to 8x13=59 please help...... fast