Math 1090.04 Homework 03
Spring 2013
Name
Student ID Number:
Instructions:
Each student is expected to follow the Homework Guidelines
described on the course webpage
• Solve the Part A Problems on your own paper.
• Solve the Part B problems in this handout.
• Attach this handout to the front of your homework assignment
Reading Assignment:
• Chapter 1.5 - Text pages 41-26
• Chapter 1.6 - Text pages 49-56
Part A:
• Chapter 1.5 - Text pages: 46-48
Problems: 11-20, 21-25, 31-40, 41-44, 46-47, 50-56, 67-70, 71-74
• Chapter 1.6 - Text pages: 57-60
Problems: 1, 3, 5, 7, 8, 9, 11-14, 16-17, 20, 23, 28
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DO NOT WRITE IN THIS TABLE!!!
(It is for grading purposes.)
Quantity of Completed Homework Problems:
out of 89
Grade: Homework
Quiz
Review Questions:
1. Simplify the following expressions using the properties of exponents:
1
1
2
3
(a) (7x 3 )(2x 4 )
(b) (3x 3 )(4x 4 )
1
(c)
20x 2
(d)
72x 4
1
5x 4
3
1
9x 3
2
(e) (x 3 )3
4
(f) (x 5 )5
1
(g) (25x4 y 6 ) 2
1
(h) (125x9 y 6 ) 3
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Chapter 1.5: Functions
2. Find the domain of the following function: g(x) =
√
x2 − 5x − 14
3. Evaluate g(x) = x2 − 10x − 3 at the following values and simplify as much as possible:
(a) g(−1)
(b) g(2)
(c) g(−3)
(d) g(x + 2)
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Chapter 1.6: Business Applications
4. Concert promoters are willing to sell tickets at a price of $8 each if they can sell 6040
tickets; however, if they can only sell 6250 tickets they insist on charging $50 each. At
the same time, 7250 music fans are willing to purchase a ticket for $10 each, but only
7000 fans are willing to purchase a ticket if they are $20 each.
(a) Find the Demand equation described by this scenario:
(b) Find the Supply equation described by this scenario:
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(c) Estimate the market equilibrium by graphing the supply and demand equations on
the same graph.
Figure 1: Problem 4
Record your estimate here:
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(d) How many tickets can be sold and supplied for $40 per ticket.
(e) Solve the system of equations to find the market equilibrium.
(f) Is your estimate close to the actual answer? If not, can you explain why?
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5. A gasoline station has weekly costs and revenue (the money taken in by the station) that
are functions of the number of gallons of gasoline purchased and sold. If x gallons are
purchased and sold, weekly costs are given by C(x) = 1.2x + 1080 and weekly revenue
by R(x) = 1.6x
(a) What are the fixed costs? What does this number tell you?
(b) What are the variable costs? What does this number tell you?
(c) What is the marginal profit? What does this number tell you?
(d) What is the marginal revenue? What does this number tell you?
(e) What is the profit from selling 100 items? How would you interpret this solution?
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(f) What is the profit from selling 1000 items? Comparing this to (e), how would you
interpret the answer?
(g) Graph the appropriate equations to estimate the break even point
(Hint: Convert decimals to fractions)
Figure 2: Problem 5
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(h) Calculate the break-even point
(i) How does your calculated break-even point compare to your estimate? If they are
different, can you explain why?
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6. Extra Credit Challenge: You drew a graph in the problem above to estimate the
break even point - there is another graph you can draw to come up with the same estimate - What is it?
If you figure it out: Include your graph and compare this estimate to your actual solution
and your previous estimate.
Figure 3: Problem 6