Math 1090 Final Exam 27 April, 2012
Name:
Teacher:
U.I.D.:
Instructions:
• Show all work as partial credit will be given where appropriate.
• If no work is shown, there may be no credit given.
• All final answers should be written in simplified form.
• You may use a scientific calculator, but no cell phone, graphing, or programmable calculators are allowed.
• You may NOT ask questions during the exam. If you think there is an error, write a note on that problem indicating your concern.
Question Points Score
1 15
2
3
15
15
10
11
8
9
Total:
6
7
4
5
15
15
20
15
10
10
10
10
150

Math 1090 Final, Page 2 of 13 27 April, 2012
1. (15 points) Market research has determined that consumers will purchase 8,000 copies of a book if it is priced at $52. If the price is lowered to $7, then the research indicates that consumers will purchase 32,000 copies of the book.
(a) Find the demand equation for the book. (Assume demand is linear.)
(b) Suppose the supply equation is given by p =
17
8000 q + 3
Find the equilibrium point.

Math 1090 Final, Page 3 of 13 27 April, 2012
2. (15 points) Let the region R be determined by the following inequalities: x ≥ 4 y ≥ 0 x + y ≤ 12
(a) Sketch the triangular region R and label each vertex, showing both its x - and y coordinate.
(b) What is the maximum value of the objective function P = 2 x + 4 y in the region R ?

Math 1090 Final, Page 4 of 13 27 April, 2012
3. (15 points) Given the following matrices, perform the indicated operations. If not possible, state the reason why.
A =
4 1
3 2
B =
5 9
0 7
 1 3 
C =

3 4

5 6
(a) Give the size of each matrix.
(b) Calculate A + B T
(c) Calculate C · A
(d) Calculate A · C

Math 1090 Final, Page 5 of 13
4. (15 points) (a) Find the inverse of
A =
4 − 3
− 5 4
27 April, 2012
(b) Solve the following system of equations:
4 x − 3 y = 23
− 5 x + 4 y = 10

Math 1090 Final, Page 6 of 13 27 April, 2012
5. (15 points) Let f ( x ) =
√ x + 1 and g ( x ) = ( x − 2) 3 + 5. Compute the following:
(a) ( f g )(3)
(b) ( g − f )( x )
(c) ( f ◦ g )(1)
(d) ( g ◦ f )( x )
(e) g
− 1
( x )
(f) The domain of f ( x )

Math 1090 Final, Page 7 of 13
6. (20 points) Solve the following equations:
(a)
4 x
2
+ 6 x = 4
27 April, 2012
(b) x (5 x + 6) = 15

Math 1090
(c)
Final, Page 8 of 13 log
2
(3 x − 2) − 2 log
2 x = 0
27 April, 2012
(d) (Give an exact answer!)
3 e
2 x +1 − 1 = 11

Math 1090 Final, Page 9 of 13
7. (15 points) Consider the function f ( x ) = − 2( x − 5) 2 + 8
(a) What is the vertex of the parabola?
27 April, 2012
(b) What is the axis of symmetry?
(c) What is the y -intercept?
(d) Is the parabola concave up or concave down? (How do you know?)
(e) Is the parabola stretched or shrunk vertically? (How do you know?)

Math 1090
(f) Graph the parabola.
Final, Page 10 of 13 27 April, 2012

Math 1090 Final, Page 11 of 13
8. (10 points) Consider the function f ( x ) = 3 log( x − 4)
(a) Find the domain.
27 April, 2012
(b) Find the x -intercept(s).
(c) Sketch the graph.

Math 1090 Final, Page 12 of 13 27 April, 2012
9. (10 points) Captain Bob wants to become a pirate. In order to realise his dream, he needs $40,000 to purchase and outfit a pirate ship. He has found an account that pays
7.2% interest compounded monthly. Bob intends to make payments into the account at the end of each month. How large does each payment need to be if he wants to have enough for a pirate ship in 5 years?
10. (10 points) Captain Bill also wants to become a pirate, but he lacks Bob’s fiscal discipline. He outfits his pirate ship by taking out a $40,000 loan at 9% interest, compounded monthly. If Bill makes payments at the end of each month for five years, how much must each payment be?

Math 1090 Final, Page 13 of 13 27 April, 2012
11. (10 points) Paula received a trust fund inheritance of $60,000 on her 35 th birthday. She plans to use it to supplement her income with 80 equal quarterly payments beginning on her 65 th birthday. If money is worth 6.4% compounded quarterly, how much will she get at the end of each quarter?