Mathematics For Business: Powers, Roots, Interests, Probabilities, And Linear Relationships

Question 1: Powers and Roots

1. 

Part a

 

Part b

 

Part c

2. 

Part a

 

Part b

 

Part c

 

Part d  65,648,000 in scientific notation

3.

Part a

Part b

  

Part c

 

Part d

 

4.

Part a

 

Dividing both sides of the equation by 22000 and simplifying we obtain

 

 Introducing logs on both sides of the equation we obtain

 

Part b

At 2% interest, rule 72 confirms that it will take 36 years to double the investment.

Part c

Divide both sides by 32000 to obtain

 

 Introducing logs to both side of the equation we obtain

 

5. 

Part a

Part b

 

Part c

 

  d)

  

x	– 8	-5	0	7	12	24
y	-14	-5	10	31	46	82

6. 

Part a

Part b

 Sarah should proceed with the project. The project is viable since the NPV is positive.

7. 

Part a

We group the data in Excel using the data analysis function to obtain the table below

Range	Frequency
50	0
55	1
60	3
65	6
70	3
75	2
80	1
85	0
90	1
95	7
100	1

Part b

Then, drawing the histogram we obtain

Part c

The histogram above shows that most of the scores lie between 60-74 implying that the median lies there.

8. 

Part a

 The probability when the likelihood is impossible equals zero.

Part b

The probability when the likelihood is certain equals 1.

Part c

Probability of 0.06 as a percentage equals 

Part d

Table 1 below shows the possible outcomes when tossing a coin and throwing a dice simultaneously. H represents a head while T stands for the Tail. Also the numbers 1-6 represent the number that appears on top when a dice is thrown.

Table 1: Total possible outcomes

	1	2	3	4	5	6
H	H1	H2	H3	H4	H5	H6
T	T1	T2	T3	T4	T5	T6

9.

(1)Net Present Value

NPV is a capital budgeting technique that takes into account the time value of money when making calculations. Investors use the method as the basis for selecting or rejecting a project. As a result, NPV can be positive, negative or zero. Positive NPV implies that cash inflows are higher than cash outflows meaning that the project is viable and should be accepted. A zero NPV denotes an equal amount of cash inflows and cash outflows. A project may be considered to be acceptable when it has zero NPV. On the other hand, a project with negative NPV should be ignored since it brings losses. 

10. Reflective Log

Actually, before the semester I started I was clueless about how the semester could unfold, bearing in mind of what I overheard from our predecessors. They could instil fear in us that the course is tough. However, I was amazed to realize how simple and informative the course was. Learning about powers, simple and compound interest, probability and linear relationships in the first few classes of the semester was a bit challenging. Particularly, probability. However, after concerted efforts through topical tutorials, I was able to understand everything from the topic. This made me feel more confident about the topic. Truly, I was amazed to know that these topics are applicable in real life. Especially, the simple and compound interests which are crucial tools in financial institutions.

Throughout the next couple of classes, I was thrilled to see how simpler the classes became. I think this is attributed to the positive attitude and high self-esteem I developed with time. I could perform calculations more easily and interpret real-life word problems based on the understanding of the topics. However, I need to improve my speed, especially when using a calculator to compute the calculations.

(2) Linear relationships                                                                               

Linear relations use one or more variables where one depends on another. Almost every situation in life with an unknown quantity can be represented using linear relationships. For instance, calculating mileage rates and predicting profit. Besides, linear equations can be applied in calculating variable costs. For example, if a taxi charges $8 to pick a person from a hotel and another $0.12 per kilometre travelled. One can get a linear equation to find the total cost of the taxi over a given distance. That is, setting x to represent distance covered and setting y to represent the total cost. Therefore, the linear relationship will be y=0.12x+8