scholarly journals Exponential functions through a real-world context

2020 ◽  
Vol 3 (10) ◽  
Author(s):  
Natalija Budinski
Keyword(s):  
Exponential Function ◽  
Real World ◽  
Mathematical Knowledge ◽  
Mathematical Concept ◽  
Exponential Functions

The exponential function as a mathematical concept plays an important role in the corpus of mathematical knowledge, but unfortunately students have problems grasping it. Paper exposes examples of exponential function application in a real-world context.

scholarly journals Mathematical Functions to Model the Depth Distribution of Soil Organic Carbon in a Range of Soils from New South Wales, Australia under Different Land Uses

Soil Systems ◽  
2019 ◽  
Vol 3 (3) ◽  
pp. 46 ◽  
Author(s):  
Brian W. Murphy ◽  
Brian R. Wilson ◽  
Terry Koen
Keyword(s):  
Organic Carbon ◽  
Soil Organic Carbon ◽  
Exponential Function ◽  
Depth Distribution ◽  
Soil Depth ◽  
New South ◽  
Exponential Functions ◽  
Two Phase ◽  
Mathematical Functions ◽  
South Wales

The nature of depth distribution of soil organic carbon (SOC) was examined in 85 soils across New South Wales with the working hypothesis that the depth distribution of SOC is controlled by processes that vary with depth in the profile. Mathematical functions were fitted to 85 profiles of SOC with SOC values at depth intervals typically of 0–5, 5–10, 10–20, 20–30, 30–40, 40–50, 50–60, 60–70, 70–80, 80–90 and 90–100 cm. The functions fitted included exponential functions of the form SOC = A exp (Bz); SOC = A + B exp (Cz) as well as two phase exponential functions of the form SOC = A + B exp (Cz) + D exp (Ez). Other functions fitted included functions where the depth was a power exponent or an inverse term in a function. The universally best-fitting function was the exponential function SOC = A + B exp (Cz). When fitted, the most successful function was the two-phase exponential, but in several cases this function could not be fitted because of the large number of terms in the function. Semi-log plots of log values of the SOC against soil depth were also fitted to detect changes in the mathematical relationships between SOC and soil depth. These were hypothesized to represent changes in dominant soil processes at various depths. The success of the exponential function with an added constant, the two-phase exponential functions, and the demonstration of different phases within the semi-log plots confirmed our hypothesis that different processes were operating at different depths to control the depth distributions of SOC, there being a surface component, and deeper soil component. Several SOC profiles demonstrated specific features that are potentially important for the management of SOC profiles in soils. Woodland and to lesser extent pasture soils had a definite near surface zone within the SOC profile, indicating the addition of surface materials and high rates of fine root turnover. This zone was much less evident under cropping.

A Soil Water Characteristic Curve Model Considering Urea Concentration

2013 ◽  
Vol 798-799 ◽  
pp. 157-160
Author(s):  
You Le Wang ◽  
Dong Fang Tian ◽  
Gai Qing Dai ◽  
Yao Ruan ◽  
Lang Tian
Keyword(s):  
Experimental Data ◽  
Water Content ◽  
Soil Water ◽  
Exponential Function ◽  
Characteristic Curve ◽  
Urea Concentration ◽  
Exponential Functions ◽  
Valuable Data ◽  
Soil Water Characteristic Curve ◽  
Curve Model

A new soil water characteristic curve (SWCC) model considering urea concentration is presented in the paper. Two assumptions are used to obtain the model. One is SWCC which could be described by exponential functions in the experiments. Another is relationship between the parameters of exponential functions and urea concentration which is linear based on experimental data. In the research, we have carried out some experiments of SWCC and obtained some valuable data which could affect urea concentration. By using linear fitting, an exponential function between water content and suction and urea concentration is established.

Activities for Students: Don't Fret over Exponential Functions

2012 ◽  
Vol 106 (5) ◽  
pp. 384-388
Author(s):  
Clea L. H. Matson ◽  
Olga Grigoriadou
Keyword(s):  
Exponential Function ◽  
Exponential Functions ◽  
Electric Bass ◽  
Stringed Instruments

Have you ever wondered what determines the position of frets—the raised elements on the neck of some stringed instruments, such as guitars and the electric bass? Is there a rule that determines where each fret is placed, and, if so, what is this rule? In this musical introduction to the exponential function, we give students an opportunity to discover this rule themselves.

scholarly journals Applied mathematics and nonlinear sciences in the war on cancer

2016 ◽  
Vol 1 (2) ◽  
pp. 423-436 ◽  
Author(s):  
Víctor M. Pérez-García ◽  
Susan Fitzpatrick ◽  
Luis A. Pérez-Romasanta ◽  
Milica Pesic ◽  
Philippe Schucht ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Cancer Patients ◽  
Real World ◽  
Mathematical Knowledge ◽  
Applied Mathematics ◽  
Specific Cancer ◽  
Real World Applications ◽  
Cancer Types ◽  
Optimized Treatment

AbstractApplied mathematics and nonlinear sciences have an enormous potential for application in cancer. Mathematical models can be used to raise novel hypotheses to test, develop optimized treatment schedules and personalize therapies. However. this potential is yet to be proven in real-world applications to specific cancer types. In this paper we discuss how we think mathematical knowledge may be better used to improve cancer patients’ outcome.

scholarly journals PRELIMINARY ESTIMATION OF POSTSEISMIC DEFORMATION PARAMETERS FROM CONTINUOUS GPS DATA IN KOREA PENINSULA AND IEODO AFTER THE 2011 TOHOKU-OKI MW9.0 EARTHQUAKE

2016 ◽  
Vol XLII-4/W1 ◽  
pp. 55-59
Author(s):  
W. A. W. Aris ◽  
T. A. Musa ◽  
H. Lee ◽  
Y. Choi ◽  
H. Yoon
Keyword(s):  
Exponential Function ◽  
Deformation Characteristic ◽  
Postseismic Deformation ◽  
Tectonic Deformation ◽  
Gps Data ◽  
Research Station ◽  
Logarithmic Function ◽  
Exponential Functions ◽  
Deformation Parameters ◽  
Continuous Gps

This paper describes utilization of GPS data in Korea Peninsula and IEODO ocean research station for investigation of postseismic deformation characteristic after the 2011 Tohoku-oki Mw9.0 Earthquake. Analytical logarithmic and exponential functions were used to evaluate the postseismic deformation parameters. The results found that the data in Korea Peninsula and IEODO during periods of mid-2011 – mid-2014 are fit better using logarithmic function with deformation decay at 134.5 ±0.1 days than using the exponential function. The result also clearly indicates that further investigation into postseismic deformation over longer data span should be taken into account to explain tectonic deformation over the region.

scholarly journals Percent: A Privileged Proportion

1995 ◽  
Vol 65 (4) ◽  
pp. 421-481 ◽  
Author(s):  
Melanie Parker ◽  
Gaea Leinhardt
Keyword(s):  
Real World ◽  
Mathematical Concept ◽  
Mathematical Concepts ◽  
History Of ◽  
Multiple Uses ◽  
Multiplicative Structures

Why is percent, a ubiquitous mathematical concept, so hard to learn? This question motivates our review. We argue that asking the question is worthwhile because percent is universal and because it forms a bridge between real-world situations and mathematical concepts of multiplicative structures. The answer involves explaining the long history of the percent concept from its early roots in Babylonian, Indian, and Chinese trading practices and its parallel roots in Greek proportional geometry to its modern multifaceted meanings. The answer also involves specifying what percent is: its meaning (fraction or ratio) and its sense (function or statistic). Finally, the answer involves understanding the privileged language of percent—an extremely concise language that has lost its explicit referents, has misleading additive terminology for multiplicative meanings, and has multiple uses for the preposition of. The answer leads to speculation, in light of previous research, concerning what can be done to teach percent—and other multiplicative mathematical concepts—more effectively.

Delving Deeper: Derivatives of Generalized Power Functions

2009 ◽  
Vol 102 (7) ◽  
pp. 554-557
Author(s):  
John M. Johnson
Keyword(s):  
Power Function ◽  
Exponential Function ◽  
Power Functions ◽  
Exponential Functions ◽  
First Semester ◽  
Derivatives Of

After several years of teaching multiple sections of first-semester calculus, it was easy for me to think that I had nothing new to learn. But every year and every class bring a new group of students with their unique gifts and insights. In a recent class, after covering the derivative rules for power functions and exponential functions, I asked the class about the derivative of a function like y = xsinx, which is neither a power function (the power is not constant) nor an exponential function (the base is not constant).

Logarithmic and exponential functions —a direct approach

1959 ◽  
Vol 52 (6) ◽  
pp. 439-443
Author(s):  
C. L. Seebeck ◽  
P. M. Hummel
Keyword(s):  
Secondary School ◽  
Exponential Function ◽  
Secondary School Students ◽  
Direct Approach ◽  
Exponential Functions ◽  
School Students ◽  
Indirect Approach

A direct approach to logarithms rather than the indirect approach as an inverse of an exponential function has many advantages for teaching secondary school students.

Projects: Developing Modelers and Modeling Opportunities: The Stepping Stones Project

1997 ◽  
Vol 90 (8) ◽  
pp. 686-688
Keyword(s):  
Mathematical Modeling ◽  
Mathematics Education ◽  
Real World ◽  
Mathematical Knowledge ◽  
School Mathematics ◽  
Stepping Stones ◽  
Evaluation Standards ◽  
The Real ◽  
World Modeling

Mathematical modeling is an emerging theme in mathematics education. In addition to giving students a knowledge of the applications of mathematics and a process for applying mathematics in the “real” world, modeling offers teachers an excellent vehicle for introducing and developing students' mathematical knowledge. For these reasons, modeling occupies a prominent place in the recommendations of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989).

Using School Lunches to Study Proportion

2003 ◽  
Vol 9 (1) ◽  
pp. 17-21
Author(s):  
Tamar Lisa Attia
Keyword(s):  
Elementary Education ◽  
Real World ◽  
Nutritional Value ◽  
Sixth Grade ◽  
Mathematical Concept ◽  
School Lunches ◽  
Relevant Issue ◽  
Mathematics Class ◽  
Real World Situation

Four—I can't eat eight” is the answer that baseball's Yogi Berra is supposed to have given when asked into how many pieces he wanted his pizza cut. Although Yogi Berra must have learned during his elementary education that the fractions 4/4 and 8/8 are equivalent, his famous pizza comment could illustrate an inability to apply a mathematical concept to a real-world situation. It could also represent a failure to meet the NCTM's Connections Standard for grades 6–8 that students be able to “recognize and apply mathematics in contexts outside of mathematics” (p. 274). A project I embarked on with my sixth-grade mathematics class required applying mathematics to analyze and write about a practical and relevant issue for them: the nutritional value of their school lunches.

Sign in / Sign up

Export Citation Format

Share Document