QUESTION 1
Refer to the document World of Numbers.docx.
(a) Answer the following questions about the article “Viva la evolution”.
(i) The article states that the ENIAC cost US$6,000,000 and that your smart phone costs 17,000
times less. According to this, how much does “your smart phone cost”? Show your working. [You may ignore inflation.]
(ii) “… technological change … seems to accelerate as time goes on. So, while the development of
‘computing’ in the 19th and early 20th centuries was ‘methodical’, in the 21st century it’s ‘exponential’. Read on and prepare to amazed …”.
What does the author mean when he says “the development … it’s ‘exponential’”? Explain.
(iii) “…boasted 5 megabytes (MB) of storage and cost a cool $3,500. … in today’s money … it
equates to $700,000 per gigabyte (GB) or $700 million per terabyte (TB)!”.
Are these calculations accurate? Explain. (Adjustment has already been made for inflation.)
(b) There are many types of graph that we commonly encounter. Examples include time series,
deterministic relationships of the form y = f(x) [eg, taxi fare vs km travelled], scatterplots, frequency
distributions [histograms, bar(column) charts, frequency polygons], etc.
Look at the graph in the article “Bolt by the Numbers”. Is it a
- time series? Explain your answer.
- deterministic relationship? Explain your answer.
- scatterplot? Explain your answer.
- frequency distribution? Explain your answer.
- none of the above? Explain your answer.
QUESTION 2
For all parts of this question, show your working.
(a) A recipe calls for heating a quantity of water in a 600 watt microwave oven for 2.5 minutes. To achieve
the same heating result, for how long should the water be heated in a 1,000 watt microwave oven?
(b) Amy Schumer’s 1000 per cent pay rise for Trainwreck follow-up
“Amy Schumer is … being paid 10 times more for her next movie than for her first feature Trainwreck. That film grossed U$138.3 million worldwide but Schumer, … earned only U$300,000. The new feature project, … will net Schumer … U$5 million, a pay rise of more than 1,000 per cent.”
(i) “… a pay rise of more than 1,000 per cent.” Is this statement correct?
(ii) To 1 decimal place, what is the correct percentage?
(c) Two popular local wines are Wright’s White and Fred’s Red.
- Wright’s White is sold in a 750 ml bottle and has an ABV of 9.5%.
- Fred’s Red is sold in a 1 litre bottle and has an ABV of 12.85%.
Alcohol by volume (ABV): number of millilitres of alcohol present in 100 millilitres of the wine.
- What is the percentage difference in ABV for the two wines?
(ii) Which bottle contains more alcohol? By what percentage (to 2 decimal places)?
QUESTION 3
(a) One person reported a distance as 3,486.72 metres (x); another reported it as 3.48672 kilometres (y).
(i) How many decimal places does x have? How many does y have?
(ii) Which value is reported with more significant figures: x or y? Justify your answer.
(iii) Which value is more accurate: x or y? Justify your answer.
(b) Packaged with your HP 10bII+ Financial Calculator (and located also in the “Calculator” section on
Moodle) is a
- Quick Start Guide booklet (QSG)
- User’s Guide (UG).
When you refer to items in these guides, quote the page numbers at the bottom of the relevant page.
eg, in the QSG, p36 is indicated at the bottom of the page by . [Disregard which appears at the top of the screen.]
In answering the following questions, quote any relevant text and/or page numbers.
(i) In the Quick Start Guide, what information is provided about the number of decimal places
displayed on the calculator? Is this information accurate?
(ii) In the User’s Guide p41-3, what information is provided about the number of decimal places
displayed on the calculator? Is this information accurate?
(iii) What is the maximum number of decimal places that can be displayed on the calculator?
(iv) What is the maximum number of digits that can be displayed on the calculator?
QUESTION 4
ChemiCon manufactures industrial chemicals at its Altona factory (A) and its Berwick factory (B). Recently, the quality control department has been studying one the products – Organosol – looking at the relationship between the thickness of the liquid and the level of contaminants it contains. Test results are available from the last 80 batches (40 from each factory).
Organosol.xlsx contains the following variables.
Factory Factory A or factory B.
Thickness The thickness of the Organosol (in micro Pa).
{If you put this variable into groups (bins), use 0 up to but not including 25,
25 up to but not including 50, etc.}
Contaminants The level of contaminants in the Organosol (in ppm: parts per million).
Provide appropriate graphs and/or tables and/or calculations and/or explanations to inform ChemiCon what this set of data reveals about the level of contaminants (loc) in Organosol.
QUESTION 5
(a) (i) Solve for x:
(ii) What constraints (if any) are there on the value of a in (i)?
(b) For b ϵ (0, ∞), does (logb x)/(logb y) give the same answer no matter what is the value of b?
Show your working.
(c) Simplify the expression:
(d) The number of ants living in a tree stump t weeks after it was invaded by a rival colony is collated in
the spreadsheet Ants.xlsx.
(i) A myrmecologist described the growth in the size of the colony as ‘exponential’. Do you agree?
If you don’t agree, suggest a different description for the growth. Justify your answer.
(ii) On the basis of the data in Ants.xlsx, estimate the number of ants in the tree stump 30 weeks
after it was invaded. Explain how you obtain your answer.
QUESTION 6
For three food items, the 1985 and 2005 prices (in current $) and quantities consumed by a typical consumer are shown in Food Items.xlsx.
- With 1985 as the base year, calculate an index for 2005 that
(i) uses the Laspeyres method.
(ii) uses the Paasche method.
(iii) measures, in current (ie, nominal) dollar terms, change in the typical consumer’s budget.
- The 3 methods in (a) all represent an attempt to measure price changes for this group of items from 1985 to 2005.
(i) Briefly explain what information is conveyed by the value you obtained for the Laspeyres
index in (a)(i).
(ii) Choose any one of the methods in (a) and state one disadvantage of using it in practice.
(iii) Choose any one of the methods in (a) and state one advantage of using it in practice.
- “If inflation averages 2.5% per annum, after 15 years 31% of the real value of each dollar will be lost
and, after 28 years, 50% will be lost.” p1045, Australian Financial Planning Handbook 2015-16
(i) Are these calculations accurate? Show your working.
(ii) If inflation averages x% per annum, after 28 years 75% of the real value of each dollar will be
lost. Calculate x. Show your working.
For this problem, you MUST use Excel’s Solver. Explain how you did so. (You may use screen shots.)
QUESTION 7
TB4 p99 #6(a)&(b) together, (c).
You may use the ‘$’ sign instead of ‘£’.
Part (d) has been added below.
(d) (i) Calculate the point elasticity of demand at Q = 35.
(ii) Interpret the value you calculated in (d)(i).
(iii) Is your interpretation in (d)(ii) just an interpretation of the slope of a linear function, or is it
something different? Explain your answer.
(iv) Look at the sign of your value in (d)(i) for the point elasticity of demand. Is it the same sign as
you would expect for price elasticity of demand? Explain why(not).
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