Purpose: To use the concepts developed in Precalculus to model an actual real world relationship and make a prediction. In this case we will model global warming The data: The following table summarizes the average yearly temperature (F")and carbon dioxide emissions in parts per million (ppm) measured at Mauna Loa, Hawaii Year 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 46.23 Temperature 44.45 CO2 43.29 43.61 43.35 46.66 45.71 45.53 47.53 45.86 316.9 320.0 325.7 331.1 338.7 345.9 354.2 360.6 369.4 379.7 Emissions

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
icon
Concept explainers
Topic Video
Question
The info and question are both provided. Thank you!
Math 4b Class Project : Modeling Real World Relationships to Make Predictions
Part 3
Purpose: To use the concepts developed in Precalculus to model an actual real world relationship and
make a prediction. In this case we will model global warming
The data: The following table summarizes the average yearly temperature (F")and carbon dioxide
emissions in parts per million (ppm) measured at Mauna Loa, Hawaii
Year
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
Temperature 44.45
43.29 43.61
43.35 46.66 45.71 45.53
47.53
45.86
46.23
CO2
316.9
320.0
325.7
331.1
338.7
345.9
354.2
360.6
369.4
379.7
Emissions
Defining our variables: t = years after 1960, T = Temperature, and C = CO2 emissions.
Describe the Relationship with a Quadratic Functions in vertex form
We will use the data fromn the years 1960 and 1990 for our models.
That is, for t = 0, T 44.45 and C = 316.9 while for t = 30, T = 45.53 and C = 354.2
1) Modeling Temperature
a) Use the data from 1960 and 1990 to find a quadratic function that models the
Temperature. Use the first data point as the vertex.
b) Use your quadratic function to predict the Temperature in 2005. Compare your
prediction with the actual Temperature in 200S.
c) On graph paper, plot the entire set of temperature data irom 1960 through 2005.
On the same axis, plot your function from part (a) with at least 4 actual points on
the graph to give it some adequate scale. Discuss the similarities and differences of
the graph and the data. How well does your function approximate the actual data
compared to the linear function you used in part 1?
Transcribed Image Text:Math 4b Class Project : Modeling Real World Relationships to Make Predictions Part 3 Purpose: To use the concepts developed in Precalculus to model an actual real world relationship and make a prediction. In this case we will model global warming The data: The following table summarizes the average yearly temperature (F")and carbon dioxide emissions in parts per million (ppm) measured at Mauna Loa, Hawaii Year 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 Temperature 44.45 43.29 43.61 43.35 46.66 45.71 45.53 47.53 45.86 46.23 CO2 316.9 320.0 325.7 331.1 338.7 345.9 354.2 360.6 369.4 379.7 Emissions Defining our variables: t = years after 1960, T = Temperature, and C = CO2 emissions. Describe the Relationship with a Quadratic Functions in vertex form We will use the data fromn the years 1960 and 1990 for our models. That is, for t = 0, T 44.45 and C = 316.9 while for t = 30, T = 45.53 and C = 354.2 1) Modeling Temperature a) Use the data from 1960 and 1990 to find a quadratic function that models the Temperature. Use the first data point as the vertex. b) Use your quadratic function to predict the Temperature in 2005. Compare your prediction with the actual Temperature in 200S. c) On graph paper, plot the entire set of temperature data irom 1960 through 2005. On the same axis, plot your function from part (a) with at least 4 actual points on the graph to give it some adequate scale. Discuss the similarities and differences of the graph and the data. How well does your function approximate the actual data compared to the linear function you used in part 1?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 3 images

Blurred answer
Knowledge Booster
Application of Algebra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,