exponential function
Variable-exponent mathematical curve
An exponential function is a mathematical function where a constant base is raised to a variable exponent, typically written f(x) = aˣ.
The defining feature is that the rate of change is proportional to the function's current value—doubling repeatedly rather than adding.
This produces the dramatic curves of compound interest, population growth, and radioactive decay.
In casual use, people say something grows exponentially to mean very rapidly, though mathematicians wince at the imprecision.
Increase in inhabitants over time
- compound interestReturns on reinvested earnings
- doubling timeTime to grow twofold
- bacterial growthIncrease in microorganism population
- MalthusianExpecting resource-outpacing reproduction
carrying capacity · viral spread · epidemic · proliferation · snowball effect · Moore's law · geometric progression · runaway growth
Returns on reinvested earnings
- interest rateCost of borrowing money
- principalChief school administrator
- present valueCurrent equivalent of future sum
- future valueAmount after growth
annuity · amortization · yield · return on investment · inflation · discounting · APR · APY
Visual data display
- asymptoteUnreached bounding curve
- y-interceptVertical axis crossing point
- monotonicUnchanging in direction
- concavityInward-curving surface quality
smooth · continuous · steep · inflection point · tangent line · domain · range · intercept
Function's rate of change
- integralAntiderivative or crucial component
- differentiationRecognizing meaningful differences
- integrationCombining into a whole
- chain ruleComposite function derivative method
limit · continuity · antiderivative · natural logarithm · slope · rate of change · differential equation
Period for fifty-percent reduction
- radioactive decayUnstable atoms releasing energy
- carbon-14Radioactive isotope for dating
- radiocarbon datingDetermining age via isotope decay
- isotopeElemental variant by mass
nuclear decay · damping · attenuation · cooling · decreasing · depreciation · atmospheric pressure · pharmacokinetics
population growth
Increase in inhabitants over time
- compound interestReturns on reinvested earnings
- doubling timeTime to grow twofold
- bacterial growthIncrease in microorganism population
Malthusian · carrying capacity · viral spread · epidemic · proliferation · snowball effect · Moore's law · geometric progression · runaway growth · explosion
compound interest
Returns on reinvested earnings
- interest rateCost of borrowing money
- principalChief school administrator
- present valueCurrent equivalent of future sum
future value · annuity · amortization · yield · return on investment · inflation · discounting · APR · APY · loan
graph
Visual data display
- asymptoteUnreached bounding curve
- y-interceptVertical axis crossing point
- monotonicUnchanging in direction
concavity · smooth · continuous · steep · inflection point · tangent line · domain · range · intercept · plotting
derivative
Function's rate of change
- integralAntiderivative or crucial component
- differentiationRecognizing meaningful differences
- integrationCombining into a whole
chain rule · limit · continuity · antiderivative · natural logarithm · slope · rate of change · differential equation
half-life
Period for fifty-percent reduction
- radioactive decayUnstable atoms releasing energy
- carbon-14Radioactive isotope for dating
- radiocarbon datingDetermining age via isotope decay
isotope · nuclear decay · damping · attenuation · cooling · decreasing · depreciation · atmospheric pressure · pharmacokinetics
- functionssubroutine, handler, lambda, procedure, closure
- mathematical functionslogarithm, trigonometric functions, linear functions, quadratic functions, inverse functions
- exponentse, squared, cubed, power of two, power of ten
- smooth functionssine, cosine, tangent, polynomial, logarithm
- EulerEuler line, Euler's formula
exponential functionlinear function
Equation producing straight graph
linear growth · polynomial function · flat line · diminishing returns · slow growth
exponential functionlogarithm
Exponent-determining mathematical operation
natural logarithm · common logarithm · ln · polynomial function · linear function
function, functional, malfunction, expound, exponent, functionality, dysfunctional, functionally, exponential