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.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I.
Describe the Relationship with a Quadratic Functions in standard form
We will use the data from the years 1960, 1990, 2005, for our models.
That is, for t = 0, T = 44.45 and C = 316.9 and for t = 30, T = 45.53 and C = 354.2, etc.
3) Modeling Temperature
a) Use the data from 1960, 1990, and 2005 to find a quadratic function
T= at +bt+c that models the Temperature in terms of the years since 1960.
b) Use your quadratic function to predict the Temperature in 2020.
c) On graph paper, plot the entire set of temperature data from 1960 through 2020.
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 and the quadratic function in
vertex form in Part 2 #1?
4 Modeling CO2 emissions
d) Use the data from 1960, 1990, and 2005 to find a quadratic function
C= at+bt+c that models the CO2 emissions in terms of the years since 1960.
(Hint: Plug in each data point to get a system of equations. Solve the system to find
a, b, and c.)
e) Use your quadratic function to predict the CO2 emissions in 2020.
f) On graph paper, plot the entire set of CO2 emissions data from 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 and the quadratic function in
vertex form in Part 2 #1?
Transcribed Image Text:I. Describe the Relationship with a Quadratic Functions in standard form We will use the data from the years 1960, 1990, 2005, for our models. That is, for t = 0, T = 44.45 and C = 316.9 and for t = 30, T = 45.53 and C = 354.2, etc. 3) Modeling Temperature a) Use the data from 1960, 1990, and 2005 to find a quadratic function T= at +bt+c that models the Temperature in terms of the years since 1960. b) Use your quadratic function to predict the Temperature in 2020. c) On graph paper, plot the entire set of temperature data from 1960 through 2020. 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 and the quadratic function in vertex form in Part 2 #1? 4 Modeling CO2 emissions d) Use the data from 1960, 1990, and 2005 to find a quadratic function C= at+bt+c that models the CO2 emissions in terms of the years since 1960. (Hint: Plug in each data point to get a system of equations. Solve the system to find a, b, and c.) e) Use your quadratic function to predict the CO2 emissions in 2020. f) On graph paper, plot the entire set of CO2 emissions data from 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 and the quadratic function in vertex form in Part 2 #1?
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
CO2
43.29 43.61
43.35
46.66 45.71
45.53
47.53
45.86
46.23
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.
%3D
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 CO2 43.29 43.61 43.35 46.66 45.71 45.53 47.53 45.86 46.23 316.9 320.0 325.7 331.1 338.7 345.9 354.2 360.6 369.4 379.7 Emissions Defining our variables: t = years after 1960, T = Temperature, and C = CO2 emissions. %3D
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