1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
DENIUS [597]
2 years ago
12

Mr. Nicholson accepts a job that pays an annual salary of $60,000. In his employment contract, he is given the option of choosin

g a) an annual raise of $3,500 or b) an annual raise of 5% of his current salary.
a) Model each of Mr. Nicholson’s salary options with a recursive sequence that includes his potential earnings for the first three years of employment.
b) According to the first three terms of each sequence, can you conclude that there is a significant difference in Mr. Nicholson’s potential earnings with each increase option? Use complete sentences to explain your conclusion.
Mathematics
1 answer:
Andre45 [30]2 years ago
8 0

Answer:

1. Arithmetic: Add 3,500

The annual raise of 3,500 means add 3,500 to the previous year's salary

60,000 + 3,500 = 63,500

63,500 + 3,500 =  67,000

67,000 + 3,500 = 70,500

70,500 + 3,500 = 74,000

74,000 + 3,500 = 77,500

Geometric: Multiply by 1.05

The annual raise by 5% of his current salary means multiply by 1.05.

60,000 x 1.05 = 63,000

63,000 x 1.05 = 66,150

66,150 x 1.05 = 69,457.50

69,457.50 x 1.05 = 72,930.38 rounded

72,930.375 x 1.05 = 76,576.89

The first sequence is arithmetic because we add the same number (3,500) to the preceding term. The second sequence is geometric because we multiply the preceding term by the same number always (1.05.)

2a. Arithmetic - New salary is $3,500 greater each year than last year's salary

S = 60,000 + 3500(n-1)

Geometric - New salary is 5% more each year than last year's salary

60,000 + (1.05)^(n-1)

2b. Arithmetic Earnings over 3 years

60,000 + 63,500 + 67,000 = 190,500

Geometric Earnings over 3 years

60,000 + 63,000 + 66,150 = 189,150

There is a 1,000 dollar difference. In this case, the arithmetic increase of 3,500 dollars would be better for Mr. Nicholson. 1,000 dollars may or may not be considered a big difference. In my opinion, I'd say there is a slight difference between the two

3.Arithmetic

a(9) = 3,500 + a(9-1)

a(9) = 3,500 + 89,000

a(9) = 92,500

Geometric

a(9) = 1.05 x a(9-1)

a(9) = 1.05 x 84,425.90

a(9) = 88,647.20

4. In this case, both the 3 year and 9 year time frames favor the arithmetic increase of $3,500. At 3 years, he would have 190,500 compared to the geometric salary of 189,150. However, this is a small difference. If he is going to be at the company for 9 years, then definitely he should choose the first opportunity. 92,500 is significantly more money than 88,647.20. So, longer time frames only make the first opportunity, which is better to begin with, shine even more.

Step-by-step explanation:

Pls brain list

You might be interested in
Y=2x-5 -3x - 4y=-2
Whitepunk [10]

Answer:

y=-x/5 =3/5. that is how it is.

8 0
2 years ago
Tim wants to build a rectangular fence around his yard. He has feet of fencing. If he wants the length to be twice the width, wh
Citrus2011 [14]

Answer:

how many feet of fencing does he have?

\

Step-by-step explanation:

8 0
3 years ago
A card is drawn from a 52 card deck any fair coin is flipped what is the probability of getting Jack and hits
Black_prince [1.1K]

Answer:

1/26

Step-by-step explanation:

There are 4 Jacks in every deck of cards, one for each suit. Therefore your chances of drawing a Jack, or any other card for that matter, are 4 in 52. So, the first probability for cards is 4/52.

Now, for the coin, the probability is 1/2.

So, the probability of getting Jack and hits is 4/52 X 1/2 = 1/26.

4 0
2 years ago
Through: (2, 2), parallel to y = x +4​
dexar [7]

Answer:

y = x

Step-by-step explanation:

We can use slope-point form.

(y-y1) = m(x-x1)

m is a slope. If the line is parallel than slopes are the same.

y = x + 4, for this line slope = 1, so for line we have to find slope is also 1.

(y-y1) = m(x-x1)

m=1, x1 = 2, y1 = 2

(y - 2) = 1(x-2)

y - 2 = x - 2

y = x

8 0
2 years ago
What fraction of 60 is 18
nordsb [41]
10/3 

hope this helped
3 0
2 years ago
Other questions:
  • Adam borrowed money to buy a new car. the bank now has a lien. what can happen if Adam doesn't make his payments on time?
    15·2 answers
  • you and your friend share a package of candies. You eat twice as many candies as your friend. If there were 36 candies in the ba
    5·1 answer
  • A circular running track is 1/4 mile long. Elena runs on this track, completing each lap in 1/20 of an hour. What is her speed?
    9·1 answer
  • Need help pleaseeeeeeeeeeee
    10·1 answer
  • Are these correct ?
    8·2 answers
  • BRAINLIEST
    12·2 answers
  • In trying to calculate the product of 5 and 12
    7·2 answers
  • Find the area of the following shapes: c
    12·1 answer
  • Simplify each algebraic expression 5a+5b-4(a+b)
    10·2 answers
  • mr. larsen's third grade class has 22 students, 12 girls and 10 boys. two students must be selected at random to be in the fall
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!