|
gptkbp:instanceOf
|
gptkb:Mathematical_Function
|
|
gptkbp:basisFor
|
a
|
|
gptkbp:codomain
|
gptkb:Positive_Real_Numbers
|
|
gptkbp:continuity
|
True
|
|
gptkbp:definedIn
|
a > 0, a ≠ 1
|
|
gptkbp:domain
|
gptkb:Real_Numbers
|
|
gptkbp:form
|
f(x) = a^x
|
|
gptkbp:hasApplication
|
gptkb:Differential_Equations
Population Growth
Radioactive Decay
Compound Interest
|
|
gptkbp:hasGraphShape
|
gptkb:Exponential_Curve
|
|
gptkbp:hasLimitAtInfinity
|
Depends on base a
|
|
gptkbp:hasModel
|
gptkb:Exponential_Decay
gptkb:Exponential_Growth
|
|
gptkbp:hasProperty
|
f(x+y) = f(x)f(y)
|
|
gptkbp:hasSpecialCase
|
gptkb:Natural_Exponential_Function
|
|
gptkbp:hasTaylorSeries
|
e^x = 1 + x + x^2/2! + x^3/3! + ...
|
|
gptkbp:inverseFunction
|
gptkb:Logarithmic_Function
|
|
gptkbp:isAnalyticFunction
|
True
|
|
gptkbp:isComplexValued
|
True
|
|
gptkbp:isDefinedOn
|
Complex Numbers
|
|
gptkbp:isDifferentiable
|
True
|
|
gptkbp:isEntireFunction
|
True
|
|
gptkbp:isEvenFunction
|
False
|
|
gptkbp:isInjective
|
True
|
|
gptkbp:isMonotonic
|
True
|
|
gptkbp:isOddFunction
|
False
|
|
gptkbp:isOneToOne
|
True
|
|
gptkbp:isRealValued
|
True
|
|
gptkbp:isStrictlyDecreasing
|
if 0 < a < 1
|
|
gptkbp:isStrictlyIncreasing
|
if a > 1
|
|
gptkbp:isSurjective
|
False
|
|
gptkbp:isTranscendentalFunction
|
True
|
|
gptkbp:notableDerivative
|
f'(x) = a^x ln(a)
|
|
gptkbp:solvedBy
|
dy/dx = ay
|
|
gptkbp:usedIn
|
gptkb:Signal_Processing
gptkb:Physics
gptkb:Calculus
Computer Science
Economics
Engineering
Finance
Biology
Statistics
Probability Theory
Demography
|
|
gptkbp:bfsParent
|
gptkb:Analytic_Functions
|
|
gptkbp:bfsLayer
|
7
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Exponential Function
|