Relax. You have done problems like these before. Even if these problems look a bit different, just do what you can. If you’re not sure of something, please ask! You may use your calculator. Please show all of your work and write down as many steps as you can. Don’t spend too much time on any one problem. Do well. And remember, ask me if you’re not sure about something.
As you work, make a “don’t forget” list of any information you need to look up or ask about.
1.
Forde collects miniature cars, each weighing 1.76 ounces. His car box weighs 4 ounces when empty. The total weight \(T\) ounces of Forde’s car box depends on the number of cars \(C\) according to the equation
\begin{equation*}
T=4+1.76C
\end{equation*}
(a)
Make a table of values showing the weight if the box contains 1, 5, 12, or 20 cars.
(b)
Draw a graph illustrating the dependence.
(c)
How many cars can Forde fit in the box and stay under 3 pounds (that is 48 ounces)? Figure out the answer and mark the corresponding point on your graph.
2.
Will women ever run the marathon as fast as men do? The world records are getting close. In 2012 the men’s record was 2:03:38 and the women’s record was 2:15:25, about 12 minutes apart! On the other hand, the record is changing very slowly. Estimates for the men’s time shows about 13 seconds drop per year on average. Estimates for the women’s time shows about 26 seconds drop per year on average.
(a)
Write an equation for each function: men’s and women’s. The variables are marathon times (in seconds) and years (measured in years since 2012). Note that 2:03:38 = 7,418 seconds and 2:12:25 = 7,945 seconds.
(b)
Use successive approximate to estimate when the women’s record might equal the men’s record. Display your guesses in a table.
(c)
Set up and solve a system to find exactly when the women’s record might equal the men’s record.
3.
An online music club charges a monthly enrollment fee plus $0.95 per album you download. Last month Andrew downloaded 31 albums for a total cost of $49.00.
(a)
What is the monthly enrollment fee?
(b)
Name the variables, including units, and write an equation relating them.
(c)
If Andrew’s bill next month is for $87.95, how many albums did he download? Show how to solve the equation.
4.
A report shows September sea-ice declining in the Northern hemisphere. In 1980 the extent of the sea-ice was 3.1 million square miles. By 2012, the sea-ice extended only 1.7 million square miles. For this problem, suppose that the area of sea-ice decreases linearly.
(a)
Name the variables, including units.
(b)
What is the rate of sea ice decrease?
(c)
Write a linear equation relating your variables.
(d)
Scientists are concerned that if the September sea-ice falls between 200,000 and 500,000 square miles, then other climate feedbacks will lead to no more sea-ice in September. According to your equation, in what year is this expected to occur? Set up and solve an inequality to answer the question.
5.
As people age they experience some hearing loss. A study was done to determine the comfort level of sound for people of different ages, meaning the loudest sound (in decibels) that the person could listen to comfortably. The data are given in the table.
Name
Akbar
Javier
Walter
Xang
Rolf
Derrick
Iago
Raheem
Age
45
45
55
65
75
75
85
85
Comfort level
58
61
63
71
75
80
82
79
(a)
Make a scatterplot showing the data. Scale your axes to start at 40 years and start the level at 55 decibels. Spread out your scale to get a large, detailed graph.
(b)
Draw the line through the points listed for Xang and Rolf. Explain why that line does not fit the data well. Label this line B.
(c)
The “best-fitting line” from statistics has equation
where \(A\) is the person’s age (in years) and \(C\) is the comfort level (in decibels). Make a table showing the values of \(C\) when A = 40, 60, and 80. Use those points to add this “best-fitting line” to your graph.
