There are 10 questions in total each worth one mark. This includes Question 6 (part (i) - part (iii)).
Question 1: Solve the following equation:
9 + 3 e ^{2 x + 1} = 12 − e ^{2 x + 1}
Choose the correct answer (A - E):
Question 2: Solve the following equation:
6 + log ( 16 x 2 − 64 ) = log ( 4 x + 8 ) + 8
A . x = 5.456
B . x = 3.859
C . x = 3.847
D . x = 27
Choose the correct answer (A - E):
Question 3: Simplify the following to a single term
4 log x + log ( 1000 x ) − 3 log ( 100 x )
Choose the correct answer (A - E):
Question 4: Given the supply and demand functions,
P S = Q S 2 + 22 Q s + 40 and P D = − Q D 2 − 10 Q D + 200
calculate the economically meaningful equilibrium quantity
Choose the correct answer (A - E):<
Question 5: The demand and supply functions for a good are
P d = 320 − 2 Q d and P s = 140 + 3 Q S , respectively. If the government provides a subsidy of $40 per unit sold. Outline the distribution of the subsidy, that is, calculate how much of the subsidy is received by the consumer and producer:
A: The consumer now pays $232, a decrease of $16 on the equilibrium price with no subsidy ($248) and the producer receives $272, an increase of $24 on the equilibrium price with no subsidy
Choose the correct answer (A - E):
Question 6
A TV manufacturer plans to increase its output by 8% each month. If it is now producing 400 TV’s per month.
(i) Calculate its monthly output for the 16th month
Choose the correct answer (A - E):
(ii) Calculate the month in which its output reaches 3200
Choose the correct answer (A - E):
(iii) Suppose the TV manufacturer now plans to increase its output by 100 each month. If it is now producing 250 TV’s per month, calculate the month in which its total production reaches 3000
Choose the correct answer (A-E):
Question 7
Given the demand and supply functions for a good,
P_{d} = 120 – 3Q and P_{s} = 2Q + 25, respectively.
If a tax of $15 per unit is imposed, outline the distribution of the tax, that is, calculate the tax paid by the consumer and the producer.
C: The consumer now pays $70.50, an increase of $7.5 on the original equilibrium price with no tax ( $63) while the producer now receives $55.50, a reduction of $7.5 on the original equilibrium price with no tax
D: The consumer now pays $54, a decrease of $9 on the original equilibrium price with no tax ($63) while the producer now receives $69, an increase of $6 on the original equilibrium price with no tax
Choose the correct answer (A-E):
Question 8
The sum of the first 20 terms of an arithmetic series is 280, the sum of the first 6 terms is 42. Write down the first 3 terms of the series.
Choose the correct answer (A - E):
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