1. No category

AMDM Unit 5 Review: Modeling
Name: ____________
1) Tell whether the following points form a linear or exponential function.
a)
b)
x
2
5
8
11
14
y
48
24
12
6
3
x
1
2
3
4
5
y
24
22
20
18
16
2) Letter grades are assigned using the following scale: 0 through 69 is an F, 70 through 79 is a C, 80 through 89 is a B,
and 90 through 100 is an A. Which type of function does this best represent?
3) What type of function can be used to represent the following:
a) The amount paid to get into an amusement park
b) Heating and air conditioning bills over the course of years
c) An illness or epidemic
d) Population of a city
4) Are the days shorter or longer in the summer time as you move further north in latitude? How about in the winter time?
5) Enter the data set below into a graphing calculator. Make a scatterplot and perform a linear regression analysis. Compare the
graph and the correlation coefficient, r. Describe how the value r describes the strength and direction of the relationship between the
variables. Use the model to predict f(12).
x
-2
0
1
5
7
y
10
1
8
-3
5
6) Given below is a scale for rating the strength of a tornado based upon wind speeds. In this example, assume that wind
speeds are always rounded up to a whole mph.
Tornado F-Scale
F0
Small Tornado
40-72 mph
F1
Medium Tornado
73-112 mph
F2
Large Tornado
113-157 mph
If wind speed is the x-variable, what is the appropriate way to state the domain for an F2 tornado
7. As the temperature gets warmer, snowy tree crickets chirp faster. You can actually use a snowy tree cricket’s rate of
chirping per minute to determine the approximate temperature in degrees Fahrenheit.
Use the table to help you answer the following questions. (3 points each)
Snowy Tree Cricket’s Rate of Chirping
Temp. °F
50
55
60
65
70
75
80
Rate (Chirps/
30
50
70
90
110
120
150
min)
A.
Identify the independent and dependent variables.
B. Write a formula for the sequence by performing linear regression on the calculator.
C. If the snowy cricket chirps 16 times, what is the approximate temp?
D.
If the temperature is 92°F, about how many times will the cricket chirp?
E. At what temperature do the crickets stop chirping?
8) An economist consulted by your temporary employment agency indicates that the demand for temporary employment (measured in
thousands of job applications per week) in your county can be modeled by the function
d = 4.3sin(0.82t + 0.3) + 7.3
Graph the function:
a) What is the amplitude of the function?
b) What is the period of the function?
c) What are the maximum and minimum values for employment?
.
9) In the Texas Hurricanes Problem where Saffir-Simpson Categories were assigned, is the graph discrete or
continuous? Why or why not? (4 points)
10) Construct a graph of the piecewise function on the interval 0 < x < 12 where:
Evaluate f(6) and f(8).
11) Use the piecewise function below, to answer the questions: (2 points each)
COST
($)
Weight (ounces)
a. How much does a 10.2 ounce package cost to ship?
b. How much does an 5 ounce package cost to ship?
c.
How much would you predict a 20 ounce package to cost?