CK12 Calculus - Single Variable

givesus

y

So the solutionto the equation has the form The box belowsummarizesthe
detailsof this function.

The Law of ExponentialGrowthand Decay

The function is a modelfor exponentialgrowthor decay, depending

on the valueof

• If : The functionrepresentsexponentialgrowth(increase).


• If : The functionrepresentsexponentialdecay(decrease).
  Where is the time, is the initialpopulationat and is the population
  after time

Applicationsof Growthand Decay
RadioactiveDecay
In physics,radioactivedecayis a processin whichan unstableatomicnucleuslosesenergyby emitting
radiationin the formof electromagneticradiation(like gammarays)or particles(suchas beta and alpha
particles).Duringthis process,the nucleuswill continueto decay, in a chainof decays,until a new stable
nucleusis reached(calledan isotope).Physicistsmeasurethe rate of decayby the time it takesa sample
to lose half of its nucleidue to radioactivedecay. Initially, as the nucleibeginsto decay, the rate startsvery
fast and furious,but it slowsdownover time as moreand moreof the availablenucleihavedecayed.The
figurebelowshowsa typicalradioactivedecayof a nucleus.As you can see, the graphhas the shapeof
an exponentialfunctionwith