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BEA1009 Introduction To Quantitative Methods

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? Keep a copy of your assignment (just in case!) In this assessment 5 marks .
(10%) are awarded for your ability to communicate mathematically, please see your Unit Outline or the Assessment folder in MyLO Content for more information. Mathematical Communication Mark: (to be completed by your tutor) 5 Page 2 of 7 1. Simplify the following:
a) 5???? 3 − (2???? + 1) 6???? (3 marks)
b) (4???? 6????) −2 (???? 3???? 2 ) 4 (4 marks) Page 3 of 7
c) Express your answer using positive indices only. 15???? 4???? 2 ???? ???????? ÷ 3???? 5???? 5 ???? 2 ????(???? 2????) 3 (4 marks)
2. Find the value of t in the following equations a) 6 4????−7 = 216 (3 marks) b) 9 2????+8 × 81(−5????) = 1 (4 marks) Page 4 of 7 3. Given the exponential model: ???? = 75(1.5) ????
a) Does this model represent an exponential growth or decay? Justify your answer. (1 mark)
b) What is the initial value? (1 mark)
c) Sketch the graph of the equation indicating the coordinates of the y-intercept. (2 marks)
d) What is the percent rate of change? (2 marks)
e) Evaluate the equation for ???? = 7 Give your answer to 2 decimal places (2 marks) Page 5 of 7 4. A house in Queensland has about 1,150 termites in its foundations (not good news for the owners!).
The termite population grows at a rate of about 2.25% per day.
a) Write an equation that models the growth of the termite population over time. Clearly define any variables you use. (2 marks)
b) How many termites does the model predict there will be in 12 weeks’ time if the house remains untreated? Give your answer to the nearest whole number. (2 marks)
5. a) Write the following as a logarithm: ???? ???? = 121 (1 mark)
b) Simplify the following (i.e. write as a single logarithm): 4 log3(????) − log3(???? 2???? 5 ) (3 marks) Page 6 of 7
6. A company writes off 6.4% per annum for one of its storage sheds with the current value of $190 000. Which method gives the greatest depreciation over 5 years , and by how much? You should use relevant calculations to support your answers. (3 marks)
7. Sarah has just won $75 000 on a scratch card (lucky Sarah!). She decides to spend $17 000 straight away to pay off her car and go on a holiday, and invest the rest in a fixed term account for 1 year to use as a house deposit later on. Sarah has the choice of accounts that offer
(i) simple interest at 3.80%,
(ii) 3.75% with interest compounded weekly or
(iii) 3.73% with interest compounded daily. Which account should she choose? Justify your answer with relevant calculations. (4 marks) Page 7 of 7 8.
a) State the ???? ????? rule for the following sequence, then use your rule to find the 36th term. {5, 12, 19, 26, 33 … } (2 marks)
b) In a geometric series the first term is 1250 and the common ratio is 3 5 . Find the sum of the first 5 terms.
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