Whole numbers<span><span>\greenD{\text{Whole numbers}}Whole numbers</span>start color greenD, W, h, o, l, e, space, n, u, m, b, e, r, s, end color greenD</span> are numbers that do not need to be represented with a fraction or decimal. Also, whole numbers cannot be negative. In other words, whole numbers are the counting numbers and zero.Examples of whole numbers:<span><span>4, 952, 0, 73<span>4,952,0,73</span></span>4, comma, 952, comma, 0, comma, 73</span>Integers<span><span>\blueD{\text{Integers}}Integers</span>start color blueD, I, n, t, e, g, e, r, s, end color blueD</span> are whole numbers and their opposites. Therefore, integers can be negative.Examples of integers:<span><span>12, 0, -9, -810<span>12,0,−9,−810</span></span>12, comma, 0, comma, minus, 9, comma, minus, 810</span>Rational numbers<span><span>\purpleD{\text{Rational numbers}}Rational numbers</span>start color purpleD, R, a, t, i, o, n, a, l, space, n, u, m, b, e, r, s, end color purpleD</span> are numbers that can be expressed as a fraction of two integers.Examples of rational numbers:<span><span>44, 0.\overline{12}, -\dfrac{18}5,\sqrt{36}<span>44,0.<span><span> <span>12</span></span> <span> </span></span>,−<span><span> 5</span> <span> <span>18</span></span><span> </span></span>,<span>√<span><span> <span>36</span></span> <span> </span></span></span></span></span>44, comma, 0, point, start overline, 12, end overline, comma, minus, start fraction, 18, divided by, 5, end fraction, comma, square root of, 36, end square root</span>Irrational numbers<span><span>\maroonD{\text{Irrational numbers}}Irrational numbers</span>start color maroonD, I, r, r, a, t, i, o, n, a, l, space, n, u, m, b, e, r, s, end color maroonD</span> are numbers that cannot be expressed as a fraction of two integers.Examples of irrational numbers:<span><span>-4\pi, \sqrt{3}<span>−4π,<span>√<span><span> 3</span> <span> </span></span></span></span></span>minus, 4, pi, comma, square root of, 3, end square root</span>How are the types of number related?The following diagram shows that all whole numbers are integers, and all integers are rational numbers. Numbers that are not rational are called irrational.
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
