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 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.

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.

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.

scholarly journals Generalized Probability Functions

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Alexandre Souto Martinez ◽  
Rodrigo Silva González ◽  
César Augusto Sangaletti Terçariol
Keyword(s):  
Exponential Function ◽  
Error Function ◽  
Generalized Functions ◽  
Probability Density Functions ◽  
Density Functions ◽  
Logarithmic Function ◽  
Rank Distribution ◽  
Exponential Functions ◽  
Generalized Exponential Function ◽  
Generalized Probability

From the integration of nonsymmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. Motivated by the mathematical curiosity, we show that these generalized functions are suitable to generalize some probability density functions (pdfs). A very reliable rank distribution can be conveniently described by the generalized exponential function. Finally, we turn the attention to the generalization of one- and two-tail stretched exponential functions. We obtain, as particular cases, the generalized error function, the Zipf-Mandelbrot pdf, the generalized Gaussian and Laplace pdf. Their cumulative functions and moments were also obtained analytically.

scholarly journals A characterization of postcritically minimal Newton maps of complex exponential functions

2018 ◽  
Vol 39 (10) ◽  
pp. 2855-2880
Author(s):  
KHUDOYOR MAMAYUSUPOV
Keyword(s):  
Exponential Function ◽  
Julia Sets ◽  
Exponential Functions ◽  
Postcritically Finite ◽  
One To One ◽  
Complex Exponential

We obtain a unique, canonical one-to-one correspondence between the space of marked postcritically finite Newton maps of polynomials and the space of postcritically minimal Newton maps of entire maps that take the form $p(z)\exp (q(z))$ for $p(z)$, $q(z)$ polynomials and $\exp (z)$, the complex exponential function. This bijection preserves the dynamics and embedding of Julia sets and is induced by a surgery tool developed by Haïssinsky.

scholarly journals Hyper Exponential Function

2020 ◽  
Vol 01 (03) ◽  
Keyword(s):  
Exponential Function ◽  
Exponential Functions

Hyper exponential functions of n-order generated by using any function f(x). n: order. j: the number of seed. x: variable. f(x): any function that is defined in an interval that contains zero. seed (x; j) = The seed of the Hyper exponential function means the first term of the series.

scholarly journals Third Hankel Determinant for A Class of Functions with Respect to Symmetric Points Associated with Exponential Function

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Exponential Function ◽  
Upper Bound ◽  
Hankel Determinant ◽  
Exponential Functions ◽  
Third Order ◽  
Symmetric Points ◽  
Class Of Functions

The purpose of the present work is to determine the possible upper bound of third order Hankel determinant for the functions starlike and convex with respect to symmetric points associated with exponential functions.

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.

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