Answered: The purpose of this analysis is to…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 19E

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Question

The purpose of this analysis is to model available atmospheric carbon dioxide data with a quadratic function of the form f(x) = ax² + bx + x. In the space below, type the model quadratic function for the relationship between year and mean carbon dioxide levels in standard mathematical form using the coefficients calculated on the spreadsheet.

Using the model equation, determine the mean atmospheric carbon dioxide levels in the year 2030.

Using the model equation, determine the mean atmospheric carbon dioxide levels in the year 2050.

What other factors might need to be taken into account to provide a more robust model to make predictions regarding future atmospheric carbon dioxide levels?

Mean Co2 Level
410 y = 0.0132x² - 51.039x +49534
390
370
350
330
310
1940 1960
1980 2000 2020 2040
Year
Mean CO2 Level
(ppm)
Poly. (Mean CO2 Level
(ppm))

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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