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gptkbp:instanceOf
|
gptkb:mathematical_concept
|
|
gptkbp:application
|
gptkb:Differential_equations
Radioactive decay
Population growth
Compound interest
|
|
gptkbp:baseRestriction
|
a > 0, a ≠ 1
|
|
gptkbp:basisFor
|
a
|
|
gptkbp:codomain
|
Positive real numbers
|
|
gptkbp:continuity
|
true
|
|
gptkbp:domain
|
Real numbers
|
|
gptkbp:fixedPoint
|
x=0, f(0)=1
|
|
gptkbp:form
|
f(x) = a^x
|
|
gptkbp:generalizes
|
Exponential map
Matrix exponential
Operator exponential
|
|
gptkbp:hasComplexExtension
|
e^{z} for z in complex numbers
|
|
gptkbp:hasPeriodicity
|
Non-periodic
|
|
gptkbp:hasSpecialCase
|
Natural exponential function
|
|
gptkbp:hasTaylorSeries
|
sum_{n=0}^∞ x^n/n!
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Exponential function
|
|
gptkbp:inverseFunction
|
Logarithmic function
|
|
gptkbp:isDifferentiable
|
true
|
|
gptkbp:isEntireFunction
|
true
|
|
gptkbp:notableDerivative
|
f'(x) = a^x ln(a)
|
|
gptkbp:notation
|
e^x
exp(x)
|
|
gptkbp:property
|
f(x+y) = f(x)f(y)
f is strictly decreasing if 0 < a < 1
f is strictly increasing if a > 1
f(-x) = 1/f(x)
f(0) = 1
|
|
gptkbp:relatedTo
|
gptkb:Euler's_formula
gptkb:Laplace_transform
gptkb:Fourier_transform
gptkb:Taylor_series
Gaussian function
Logarithm
Exponential decay
Exponential growth
Power function
|
|
gptkbp:shape
|
gptkb:Convex
Monotonic
|
|
gptkbp:solvedBy
|
dy/dx = ay
|
|
gptkbp:usedIn
|
gptkb:Physics
gptkb:Calculus
Finance
Biology
Statistics
Complex analysis
|
|
gptkbp:bfsParent
|
gptkb:Entire_Functions
|
|
gptkbp:bfsLayer
|
7
|