Deck 2: Non-Linear Equations

Question 1

If fixed costs are 30, variable costs per unit are Q + 3, and the demand function is P + 2Q = 50
Which of the following gives the formula for the associated profit?

A)47Q - 2Q2 + 33
B)47Q - 3Q2 - 30
C)49Q - 2Q2 + 33
D)49Q - 2Q2 - 33
E)53Q - 3Q2 + 30

Answer 1

B

Question 2

Find the value of k so that the equation x2 - 10x + 2k = 8x - k
Has exactly one root.

A)81
B)9
C)1
D)3
E)27

Answer 2

E

Question 3

Given the supply and demand functions P = QS2 + 10QS + 30
P = - QD2 - 8QD + 200
Calculate the equilibrium price, correct to 2 decimal places.

A)89.59
B)48.64
C)5.76
D)120.76
E)142.39

Answer 3

D

Question 4

Make x the subject of $$\begin{array} { l } y = \ln \left( 3 + e ^ { 2 x } \right) \\\text { A) } x = \frac { \ln \left( 3 - e ^ { y } \right) } { 2 } \\\text { R) } x = \frac { e ^ { y } - 3 } { 2 } \\\text { C) } x = \frac { y - \ln 3 } { 2 } \\\text { n) } x = \frac { y } { 2 \ln 3 } \\\text { F) } x = \ln \sqrt { e ^ { y - 3 } }\end{array}$$

Question 5

A firm's average cost function is given by Find, to the nearest whole number, the value of Q at the lowest point on the graph of AC plotted against Q, in the interval, 0 c Q c 30.

A)25
B)20
C)15
D)5
E)10

Question 6

The value (in cents)of shares, x years after their flotation on the stock market, is modelled by V = 6e0.8t
Find the increase in the value of these shares, to the nearest cent, 4 years and 2 months later.

A)167
B)168
C)162
D)172
E)173

Question 7

Find the solutions of the quadratic equation

Question 8

State the degree of homogeneity of the production function

Question 9

$\text { If } a=\frac{2 \sqrt{x}}{y^{3}} \text { and } b=3 x^{4} y \text {, simplify } \frac{4 b}{a^{2}} \text {. }$

A) $3 x ^ { 3 } y ^ { 7 }$
B) $6 x ^ { 3 } y ^ { 7 }$
C) $6 x ^ { \frac { 7 } { 2 } } y ^ { 4 }$
D) $3 x ^ { \frac { 7 } { 2 } } y ^ { 4 }$
E) $6 x ^ { \frac { 5 } { 2 } } y ^ { - 3 }$