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).
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?
Answer:
208 ounces in 13 pounds
Step-by-step explanation:
Unit 3 parallel and perpendicular lines homework 2 please help quickly don’t understand front page
Answer:
this statement is confusing me
Step-by-step explanation:
cause I don't understand it
Help me please i've been stuck on this question for hours.
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.
Please help me I need help
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
Answer:
Step-by-step explanation:
yes cdrj
ejkfkj
ennejw
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?
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.
Help thank you so very much
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
Answer quickly! [tex]x^{2} = 6[/tex]
[tex]x = \pm \sqrt{6}[/tex]
Dilate the figure by the scale factor. Then enter
the new coordinates.
K = 2
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 help me figure this out.
Need help with math problem
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
Find the quotient or 4/5 and 6/7 give ur answer as a fraction in simplest form
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
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.
Answer:
x = -2
Step-by-step explanation:
PLEASE, I need help ASAP !
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....
katryn owes her father $25.write this number as an integer.
Answer:
-25
Step-by-step explanation:
When you owe someone something, in integers, your answer is in the negative.
Homework help please
Answer:
h=-136
Step-by-step explanation:
..............
What is the slope of 3x+4y=−2?
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
true or false, when graphing a linear Inequality in two variables, the inequality symbol " < " states to use a broken line.
Answer:
Ture I tink
Step-by-step explanation:
HELPPPPPPPPPPPP PLEASEEEE
Answer:4
Step-by-step explanation:
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.
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.
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.
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.
Find the next term in the geometric sequence that is calculated with a common ratio of 4 if the current term is 4
Answer:
16
Step-by-step explanation:
Multiply the term (4) by the common ratio (4)
4 * 4 = 16
Find the slope and y intercept of the line 3x+2y=-6
Answer:
Step-by-step explanation:
Slope - -3/2
y-intercept- (0,-3)
Quickly answer number 10 text only no fonts (100 points) mark brainliest
25
have a great day! :3
Answer:
Hello again the square root of 625 is 25
Estimate the difference by rounding each number to the nearest whole
367.2-294.8
A. 72
B.72.4
C.73
D.80
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.
Who can help me with this entire page?
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
solve pls brainliest
Answer:
4.5341 < 6.9 < 6.906 < 6.96
Step-by-step explanation:
4.5341 is closer to 0 than 6.96 is.
CLASS 6 MATHS!!!! HELP ME PLEASE!!!!!!!
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]
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
Answer:
the answer are is c,e,h because they have low prices