Consider a harmonic signal composed of p exponential functions
with arbitrary amplitudes, phase angles and decaying factorials.
Declining trends in CSTD typically occur after use and production of a chemical has been restricted or banned, and are often fitted with exponential functions
(Craan and Haines 1998; Erdogrul et al.
Ger, On some inequalities and stability results related to the exponential function
Lutz, Exponential functions
on time scales: Their asymptotic behavior and calculation, Dynam.
The main cause for the varying performance of the outlier tests based on the Box-Cox and exponential functions
was the remaining kurtosis after the transformation of data (Fig.
Note that in all three texts the identical approach is taken for the exponential functions
The effect of graphics calculator use on precalculus students' understanding of polynomial, rational, and exponential functions
As h approaches infinity the exponential functions
In a general situation a system of exponential functions
is of the form
are commonly used to describe time-dependent physical phenomena, such as failure due to wear and tear.
Details of the website are not for the fainthearted (mathematically speaking) because its pages include the complex mathematical equations with all the variables, constants, exponential functions
5 A Calculus Approach to the Logarithm and Exponential Functions
Jurek, a math teacher, provides ready-to-use resources for middle and high school students in Algebra 1 courses organized by units on the introduction to functions and relationships, systems of linear equations, exponent rules and exponential functions
, and quadratic functions.
Scientific calculators present data in two-line displays for fast calculations of large numbers, scientific notation, trigonometric functions such as sine and cosine, and exponential functions
, including square roots, constants and logarithmic functions.
Modern mathematicians recognize this eighteenth-century wonder worker with 21 papers on such diverse topics as Euler's work from 1750 to 1760, his fourteen most significant problems, his archives, his proof, with Bernoulli, of the fundamental theory of algebra, and his work on the quadrature of lunes, the Basel problem, elliptic integrals, harmonic progressions, power series expansions of the logarithmic and exponential functions
, the summation formula, combinatories, the partition function, parallels with Clausen, the motion of the lunar apsides, elastic curves, the advection equation, the propulsion of ships and the creation of accurate maps.