Name: Melissa Stacy
MTH133
Unit 1-2 Individual Project (IP2 in Unit 2)
1. The following graph shows how a 4-color web printing press depreciates from the
year 2006 to the year 2010. It was purchased new in the year 2006;
therefore x = 0 represents the year 2006.
X – axis (horizontal) = years starting from 0 = 2006 and increasing by 0.5
years
Y – axis (vertical) = price in $ amounts
You can click and drag the
graph to enlarge it if it will
make it easier for you to
read.
a)
List the coordinates of any two points on the graph in (x, y) form.
(1.0, 114,000),(2.0, 108,000)
b)
Find the slope of this line:
Answer: -6,000
Show your work here:
Slope = (108,000-114,000)/(2-1)= -6,000
c)
Find the equation of this line in slope-intercept form.
Answer: y = -6,000x+120,000
Show or explain your work here:
Line: y= mx+n where m=-6,000
(2,108,000) is on the line then
108,000 = -6,000(2)+n
n= 108,000+2(6,000)=120,000
y=-6,000x+120,000
d)
If trend for the depreciation of the press continued, what would be its value in
the year 2015? Show how you obtained your answer using the equation you
found in part c).
Answer: 66,000
Show or explain your work here:
We have to find y when x=9 (year 2015)
Y=-6,000(9)+120,000
Y= 66,000
2. Suppose that the length of a rectangle is three cm longer than twice the width
and that the perimeter of the rectangle is 90 cm.
a)
Set up an equation for the perimeter involving only W, the width of the
rectangle.
Answer:
6w+6
Work:
Length = 2w+3 then perimeter = 2(w+2w+3)=6w+6
b)
Solve this equation algebraically to find the length of the rectangle. Find the
width as well.
Answer: Length 31 , Width 14
Show your work here:
6w+6=90 then 6w=84 then w=14 and l =2w+3 = 2(14)+3=31
3)
A temporary agency offers two payment options for administrative help:
Option1: $25 daily fee plus $10/hour; or
Option 2: No daily fee but $15/hour.
Let x = total hours worked.
a)
Write a mathematical model representing the total temp cost, C, for a
four-day temporary administrative assistant in terms of x for the
following:
Option 1: C=100+10x
Option 2: C=15x
b)
How many total hours would the temp need to work in the four day
period for the cost of option 1 to be less than option 2. Set up an
inequality and show your work algebraically using the information in
part a. Don’t forget about the daily fee in Option 1 (it’s a four day
proposition!). Do not assume an eight hour workday. Any number of
hours per day is possible.
Answer: More than 20 hours
Show your work here:
100+10x < 15x
10x-15x < -100
-5x < -100
5x > 100
x>20
4)
Use the graph of y = 7 – 6x – x2 to answer the following:
a)
Without solving the equation (or factoring), determine the solutions to the
equation 7 – 6x – x2 = 0 using only the graph.
Answer: 2 solutions
Explain how you obtain your answer(s) by looking at the graph:
We see that the graph has 2 x-intercepts
b)
Does this function have a maximum or a minimum?
Answer: Maximum
Explain how you obtain your answer by looking at the graph:
The graph goes up and down
c)
What is the equation of the line (axis) of symmetry for this graph?
Answer: x= -3
d)
What are the coordinates of the vertex in (x, y) form?
Answer: (-3,16)
5)
The profit function for the Recklus Hang gliding Service is P(x) = -0.4x2 +
fx - m, where f represents the set up fee for a customer’s daily excursion and m
represents the monthly hanger rental. Also, P represents the monthly profit in
dollars of the small business where x is the number of flight excursions facilitated
in that month.
a)
If $40 is charged for a set up fee, and the monthly hanger rental is $800;
write an equation for the profit, P, in terms of x.
Typing hint: Type x-squared as x^2
Answer: P(x)= -0.4x2+40x-800
b)
How much is the profit when 30 flight excursions are sold in a month?
Answer: 40
Show your work here:
P(30)= -0.4(30)2+40(30)-800= -360+1200-800 = 40
c)
How many flight excursions must be sold in order to maximize the profit?
Show your work algebraically. Trial and error is not an appropriate method of
solution – use methods taught in class.
Answer: 50
Show your work here:
x-coordinate of the vertex = -b/2a = -40/-0.8=50
d)
What is the maximum profit?
Answer: 200
Show your work here:
P(50) =-0.4(50)2+40(50)-800 = -1000+2000-800=200
6. Graph the equations by completing the tables and plotting the points; you may
place them on the same graph, or graph them separately. You may use Excel or
another web-based graphing utility.
a) y = 2x - 5
Use the table; find at least 3 points using any values for x.
x
y
-1
1
3
-7
-3
1
b) y = 3x - x2
Use the values of x provided in the table.
x
y
-1
-4
0
0
1
2
2
2
3
0
4
-4
c)
Place your graph(s) here: