MAT135Y5 Chapter 3.8: MAT135Y5 Chapter 3.: Chapter 3.8_ Exponential Growth & Decay
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Exponentialgrowth13decay it yet is the value of a quantity y. 0 respect to t is proportional to itssite yet time e p it therateof change ofy anytime then. In the context of population growth where dct is thesite of a population time t we canwrite defy or ptddt. Theauantltry f adf is thegrowth rate dividedbythepopulation site it is dthmthahthth mmmm. 1,7 per rate weestimatethatthe worldpopulation will be by themodelpredict that the dopulatbir in 2020 will be. Radioactivedecay it mlt is the mass remainingfrom an initial massmo ofthesubstanceafter timeltt thenthe relativedecayrate imdmhas beenfound experimentally. Instant itfollowsthat at where k is a negative constant mass decays exponentially metkmoekt. Therateofdecay is also expressed interms ofhalf life thetimerequiredforhalfof any. M t m deke 100eke the determinethe valueof k. The mass after1000 magoo 100e 11h2100011590 years is a 65mg. 100e 4h21tkao go or e un2 t11590 p z solvefors 1h21 too.