Concept explainers
a.
Find a trigonometric model for the temperatures in International Falls.
a.

Answer to Problem 84E
Explanation of Solution
Given information:
The table shows the maximum daily high temperatures (in degrees Fahrenheit) in Las Vegas
Model for the temperatures in Las Vegas is
Calculation:
We are given with the data, which shows the maximum daily high temperatures in Las Vegas L, and international falls l, in degrees Fahrenheit, for month t,
We are given with a model for the temperature in Las Vegas,
Now to model the data for international Falls,
Amplitude :
Period:
Because the maximum temperature occurs in the seventh month,
Therefore,
So,
The average temperature is
So,
Hence, the model is
b.
How well does the model fit the data?
b.

Answer to Problem 84E
Explanation of Solution
Given information:
The table shows the maximum daily high temperatures (in degrees Fahrenheit) in Las Vegas
Use a graphing utility to graph the data points and the model for the temperatures in Las Vegas. How well does the model fit the data?
Calculation:
We are given with the data, which shows the maximum daily high temperatures in Las Vegas L, and international falls l, in degrees Fahrenheit, for month t,
We are given with a model for the temperature in Las Vegas,
Let us first plot the points and graph the model Los Vegas,
Hence, the graph is plotted.
c.
How well does the model fit the data?
c.

Answer to Problem 84E
Explanation of Solution
Given information:
The table shows the maximum daily high temperatures (in degrees Fahrenheit) in Las Vegas
Use the graphing utility to graph the data points and the model for the temperatures in International Falls. How well does the model fit the data?
Calculation:We are given with the data, which shows the maximum daily high temperatures in Las Vegas L, and international falls l, in degrees Fahrenheit, for month t,
We are given with a model for the temperature in Las Vegas,
The model fit the data well.
Let us now plot the points and graphs the model of international falls,
Hence, the graph is plotted.
d.
Use the models to estimate the average maximum temperature in each city.
d.

Answer to Problem 84E
Las Vegas:
Explanation of Solution
Given information:
The table shows the maximum daily high temperatures (in degrees Fahrenheit) in Las Vegas
Use the models to estimate the average maximum temperature in each city. Which value in each model did you use? Explain
Calculation:
We are given with the data, which shows the maximum daily high temperatures in Las Vegas L, and international falls l, in degrees Fahrenheit, for month t,
We are given with a model for the temperature in Las Vegas,
Hence, The annual average temperature is
Las Vegas:
International Falls:
We used the constant term.
e.
What is the period of each model?
e.

Answer to Problem 84E
Explanation of Solution
Given information:
The table shows the maximum daily high temperatures (in degrees Fahrenheit) in Las Vegas
What is the period of each model? Are the periods what you expected? Explain.
Calculation:
We are given with the data, which shows the maximum daily high temperatures in Las Vegas
We are given with a model for the temperature in Las Vegas,
Hence, The period for both the model is
Yes, this is what we expected, as the number of months in a year is
f.
Which city has the greater variability in temperature throughout the year? Which value in each model determines this variability? Explain
f.

Answer to Problem 84E
Explanation of Solution
Given information:
The table shows the maximum daily high temperatures (in degrees Fahrenheit) in Las Vegas
Which city has the greater variability in temperature throughout the year? Which value in each model determines this variability? Explain
Calculation:
We are given with the data, which shows the maximum daily high temperatures in Las Vegas
We are given with a model for the temperature in Las Vegas,
Hence , International Falls has the greater variability,
Amplitude determines this factor.
The greater the amplitude, greater is the variability.
Chapter 4 Solutions
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