This chapter describes a wide variety of exponential behavior models, including population growth, radioactive decay, charging and discharging of capacitors, inflation and interest, and armies at war. The rate o
ExponentialGrowthandDecay指数增长和衰变
Exponential Growth and DecaySuppose y = e^{kx}. Then dy/dx=ke^{kx}. Since y=e^{kx}, dy/dx=ky. This is an example of a differential equation. If y=2e^{kx}, then dy/dx=2ke^{kx}, which is once again eq…
Exponential Growth and Decay指数增长和衰变 ExponentialGrowthandDecay Section5.7 Problem:AsinglebacteriumisinaPetridish.Every3secondsthebacteriadoubles.Findtherelationshipbetweent,thenumberofseconds,andN(t),thenumberofbacteria.t(seconds)N(t)(#ofbacteria)0369 3 N(t)2 t 12 …112121...
Recalltheformulabelow.Weuseditforexponentialdecayandgrowth.Itcanalsobeusedinhalflifeproblems.A0=initialamount(attime0)A(t)=amountaftertyears,days,etct=timeinyears,days,etck=growth/decayconstant Iodine131isaradioactivematerialthatdecaysaccordingtothefunction whereA0istheinitialamountpresentandA(t)istheamoun...
Growth and DecayBut sometimes things can grow (or the opposite: decay) exponentially, at least for a while.So we have a generally useful formula:y(t) = a × ekt Where y(t) = value at time "t" a = value at the start k = rate of growth (when >0) or decay (when <0) t =...
Exponential Growth and Decay Recall that if y=f(t)( then f)(t)=dyt is called the rate of change of y with respect to t. Another very important measure of rate of change is the relative rate of change f,(t) y, = .f(t) y. ...
What is the difference between linear and exponential? Exponential Functions. In linear functions, rate of change is constant: asx goes up, y will go up a consistent amount. In exponential functions, the rate of change increases by a consistent multiplier—it will never be the same, but there...
7-1 Exponential Functions, Growth and Decay Lesson Objective Lesson Presentation Lesson Quiz Write and evaluate exponential expressions ..
1、.Exponential Growth and DecayExponential growth and decay occurs when quantities increase or decrease proportional to the quantity present.Ex.GrowthDecaySavings AccountsRadioactive ChemicalsRRSPsCarbon DatingBacterial CulturesValue of a vehiclePopulation GrowthConsider a city thats population grows ...