mth 158
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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I have not finished all the assignments for Chapter 3. The last part of the chapter is so confusing for me that I want to see my tutor before I try and solve these. I have moved on to Chapter 4 in the meantime.
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In chapter 4, there are a lot of questions that want you to solve the problem by using a graphing utility or graphing calculator. I do not have one. Is this something that I need to get in order to finish this course? I may be able to borrow one from someone, but I don't have the finances to buy one at the moment.
I'm not big on graphing calculators for college algebra, precalculus or calculus courses.
However, the computer algebra system DERIVE is very good and is available on computers in the Learning Lab. It also appears to be available in a trial version for $2.99 at the link given below
http://derive.en.softonic.com/download
Use your own judgement about the site, but DERIVE itself is a safe product.
There is an exercise on DERIVE at my website. The URL is
http://vhcc2.vhcc.edu/pc1fall9/initial_derive_exercise.htm
This exercise takes most students a couple of hours and nearly everyone says it's well worth the time.
If you run through the exercise and let me know, I can include DERIVE-related exercises in some of my responses. Could be very helpful in understanding shifts, stretches, etc..
I have been practicing on the skill building in Chapter 4 and have a couple of questions.
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In problem 4.2.44 it states
In 2002, major league baseball signed a labor agreement with the players. In this agreement, any team whose payroll exceeds $128 million in 2005 will have to pay a luxury tax of 22.5%(for first-time offenses). the linear function T(p) = 0.225(p - 128) describes the luxury tax T of a team whose payroll is p(in millions of dollars)
a) What is the implied domain of this linear function?
Would the domain be {x| x >= 128 million} I'm not real sure of myself in finding the domain of a linear function.
That would be the appropriate domain, but the variable is p so you would write it as {p | p >= 128 million}.
If p was less than 128 million you would get a negative result, which would not make sense as a luxury tax.
b) What is the luxury tax for a team whose payroll is $160 million?
To solve this would you do the following:
T(p) = 0.225(p-128)
0.225(160 - 128)
Luxury Tax = 7.2 Million
c) Graph the linear function.
This is always the one that trips me up. How do you start to find the first point on a graph of a linear function like this? I just go blank on graphing functions unless it is something that is exactly like one of the problems from the chapter that goes over step by step how to solve.
For a linear function you could start with any point on the graph, but either the horizontal or vertical asymptote is usually a good choice.
The horizontal asymptote for a function y = f(x) occurs when y = 0. The vertical intercept occurs when x = 0.
For the function T(p) the horizontal asymptote occurs when T(p) = 0 and the vertical when p = 0.
Since p = 0 isn't in the domain of the function, you wouldn't use the vertical intercept.
The horizontal intercept occurs when T(p) = 0, and it's easy to find this value:
T(p) = 0.225 * (p = 128) so T(p) = 0 when
0.225 * (p - 128) = 0. Dividing both sides by 0.225 you get
p - 128 = 0 so that
p = 128.
Your initial point would therefore be the point (128, 0).
Of course you probably figured this out originally when you arrived at the domain {p | p >= 128 million}.
The slope of the graph is 0.225.
d) What is the payroll of a team that pays a luxury tax of 11.7 million?
T(p) = 0.225(p-128)
0.225(p - 128) = 11.7 Million
0.225p - 28.80 = 11.7
0.225p = 11.7 + 28.80
0.225p = 40.50
p = 180 Million
Question 4.2.48
Suppose a company has just purchased a new machine for its manufacturing facility for $120,000. The company chooses to depreciate the machine using the straight-line method over 10 years.
a) Write a linear function that expresses the book value V of the machine as a function of its age x.
would you first do 120,000/10 = 12,000 as the value it depreciates each year and then do the linear function as:
V(x) = -12,000x + 120,000
Exactly.
b) Graph the linear function.
Would you plot the point (0, 120,000) on a graph that has the years on the x axis from 1 to 10 and the price on the y axis as 120,000 being the y intercept. Then from there you would move 1 unit to the right (for the run) and down to the unit of measure that represented 12,000 on the y axis (for the rise)? Again, I am not sure how to graph these, but it seems a bit easier when the slope and the y intercept are given.
What you say is exactly right. That would work, and would give you an accurate graph.
Even easier for this function:
You know the value is 0 after 10 years. So the horizontal intercept is (10, 0).
You could just draw the line from (0, 120 000) to (10, 0). This line would show a decrease of $12 000 every year, and would coincide completely with a graph which is made as you describe.
c) What is the book value of the machine after 4 years?
V(x) = -12,000x + 120,000
-12,000(4) + 120,000 = $72,000 book value
d) When will the machine have a book value of $72,000?
If I did the part c correct, then it would be 4 years.
You did very well on these problems. See my notes for just a little more (as well as advice on 'graphing utility' questions).