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
Write 0.735 as a simplified fraction
Arisa [49]

Answer:

73/5

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
The population is a Midwest industrial town decreased from 224,000 to 221,000 in just 4 years. Assuming that this trend continue
valina [46]

Answer:

227750

Step-by-step explanation:

If we assume that the rate of increase in population is linear, then in 4 years the increase in population is (224000 - 221000) = 3000.

So, the rate of increase in population is \frac{3000}{4} = 750 persons per year.

Now, we have to calculate the population of the town after an additional 5 years.

So, the population in 5 years will increase by (750 × 5) = 3750

Therefore, the population after an additional 5 years will be (224000 + 3750) = 227750. (Answer)

7 0
3 years ago
A circular garden with a radius of 8 feet is surrounded by a circular path with a width of 3 feet.
Vladimir [108]

Answer:

178.98 ft2

Step-by-step explanation:

we know that

The area of the circular path alone is equal to subtract the area of the circular garden from the area of the complete circle (circular garden plus circular path)

so

A=\pi (r_2^2-r_1^2)

where

r_1=8\ ft ---> radius of circular garden

r_2=8+3=11\ ft ----> radius of the circular garden plus radius circular path

substitute

A=3.14 (11^2-8^2)=178.98\ ft^2

5 0
3 years ago
Read 2 more answers
Help pls i feel like i have the right answer but i wanna make sure
Sholpan [36]

Answer:

-43

Step-by-step explanation:

Using PEMDAS and multiplying first gives you (-5 + 7) - 45

This gives you 2 - 45 which equals -43

5 0
3 years ago
Read 2 more answers
Who will help me 30 points please help !!! 5 assignments
BartSMP [9]
The correct answers are 1. D, 2. A, 3. A, 4. A, 5. A
4 0
2 years ago
Other questions:
  • Hi. im kinda stuck on this question.
    8·2 answers
  • for a class gardening project 1/3 of mrs gordon's students planted marigolds and 1/2 planted tulips what fraction of the class p
    11·1 answer
  • what is the average speed of a train that covers 80 km in 1 hour, 200 km in 2 hours and 420 kn in 4 hours
    13·1 answer
  • Graph the system of equations -3x + y = -2
    15·1 answer
  • Casey knit a square shaped dish cloth. What is the area of the dishcloth?
    11·1 answer
  • What is the coefficient of q in the sum of (2/3q-3/4) and(-1/6q-r)?
    10·2 answers
  • A map of Australia has a scale of 1 cm to 120 km. If the distance between Melbourne and Canberra is 463 km, how far apart are th
    9·1 answer
  • Which expression is equivalent to
    12·1 answer
  • G(x)=x-3<br> h(x) = 3x + 1<br> Find (g of h)(2)
    13·1 answer
  • What conclusions can be made about the amount of money in each account if f represents Molly's account and g represents her brot
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!