Math 3
2-1 Function Family Review
Name _______________________________
One of the most basic pursuits of mathematics is to be able to model phenomena that occur in the world.
One of the most sought after phenomena to model is the stock market. Many people and companies spend a
lot of time and money trying to model and predict the behavior of the stock market. A successful model
would allow someone to make billions of dollars.
The below graph is the long range trend of the Dow Jones Industrial Average, a key index that measures
how well the stock market is doing; the higher the index, the better for investors. Take a look at the graph
and read the article below
The ability to even attempt to model such a complex graph takes quite a bit of mathematical and
statistical sophistication and understanding. In this investigation, we will begin to develop an understanding
of how “function families” can help us model real world phenomena.
Learning Goals:
 I can review and extend properties linear, exponential, and quadratic functions and their uses in
mathematical modeling

I can solve problems involving linear, exponential, and quadratic function families
Use the Chevy Camaro data on the back page of this packet to help answer this question.
I. Linear Functions
Open up a spreadsheet in your calculator and enter years 1 through 5 in column A. In column B, enter
the Fuel Cost for the first five years. Create a scatterplot. Find a model that fits the data. Record the
equation in the table below. Round to the nearest 10th.
 Repeat the process for Financing, Insurance, & Opportunity Cost.
Regression Model
Sketch of Graph
Meaning of Slope
Fuel Cost
Financing1
Insurance
What would you expect the fuel cost to be in year 8?
How many years would it take for the insurance to reach $1758?
1
Financing is an estimate of what it will cost you to borrow money to purchase a vehicle. It is basically how much you are
paying in interest over the life of the loan.
II. Exponential Functions
A. Are you already sad about how much money a new vehicle costs? It only gets worse …. Look at
the Depreciation category. Enter 0 through 5 in column A. In column B, enter the MSRP (sticker
price) into the first position (B1). The next entry in column B is how much the vehicle depreciates
in the given year – that is how much less the vehicle is worth than the year before. Enter the value of
the car after depreciation in column B (meaning subtract the depreciation figures below from the
value of the vehicle, so the entry in B2 would be $59545  $16780  $42765 ). Make a scatterplot of
the data. What type of regression this time?
Record your model (Round to the nearest 100th): ___________________________
B. How much will the car be worth in 2020?
C. In how many years will the car be worth $35,000? Hint: Find an intersection using a graph.
D. In how many years will the car be worth ½ its value?
III. Quadratic Models
Fellas, some day you are going to buy an engagement ring. The ring itself only costs between $500 and
$2000, but the diamond is a whole other story.
Two of the biggest determining factors in the price of the diamond are the weight and the color. Color is
figured on a letter scale ranging from, most the most expensive, D (colorless), to the least expensive, Z
(yellow). Weight is by the number of carats.
Since you will only want the best for your future wife, here is a price chart for D-colored diamonds.
Weight
COST
(in carats)
0.25
$415
0.50
$1052
1.00
$4419
1.50
$9243
2.00
$17,087
A. Graph the data on your calculator.
B. Is the data listed linear, exponential, or quadratic? Explain.
C. Find a regression equation that best fits the data. Write it below. Round to the nearest 100th.
E. What if you wanted a 3-carat diamond? How much would you expect it to cost, using your equation
above?
F. Jay-Z bought Beyonce an 18 carat diamond! Kanye West bought Kim Kardashian a 20.5 carat ring!
Being Jay-Z and Kanye, you can safely assume the diamonds were D-colored. Use your equation
above to find the cost of those diamonds. [If you are curious, you can look-up on-line what they
actually paid].
G. You think these prices are a little bit much for you budget, so you ask the jeweler for some help.
She says that you can save a lot of money if you are willing to compromise on the quality a little bit.
So you decide to get an I-color diamond (almost colorless). Here’s the price chart for I-color
diamonds.
Weight
COST
(in carats)
0.25
$393
0.50
$1035
1.00
$4071
1.50
$7598
2.00
$14,057
H. Graph the data on your calculator.
I. Is the data listed linear, exponential, or quadratic? Explain.
J. Write the equation of best fit
K. The “rule” is that a guy is supposed to spend two months’ salary on an engagement ring. However,
that “rule” is rarely followed in reality (sorry ladies). If your budget is $3,000, what carat I-colored
ring could you buy? What carrot D-colored ring?
I-colored __________
D-colored __________