Exponential Growth and Decay
Exponential Growth
A process exhibits exponential growth if it can be represented by a function of the form fx=c⋅ar⋅x, where c>0 and either
a>1, and r>0; or
0<a<1 and r<0.
Exponential Decay
A process exhibits exponential decay if it can be represented by a function of the form fx=c⋅ar⋅x, where c>0 and either
0<a<1, and r>0; or
a>1, and r<0.
Radioactive isotopes decay over time by emitting what physicists call alpha and beta particles and gamma rays. This is an exponential decay process.
Select an isotope from the Isotope list. The graph of its mass decay over time is shown, along with its decay equation. The coefficient r in the exponent is the isotope's decay constant, and has units of milliseconds (ms). The initial mass is 100 kg. When the time parameter, t, is measured in milliseconds, the entire equation then has units of kilograms (kg).
H[3]He[6]Li[8]Be[7]B[8]C[9]N[12]O[13]F[17]Ne[17]Na[20]Mg[20]Al[22]Si[22]P[26]S[27]Cl[31]Ar[30]K[35]Ca[35]Sc[40]Ti[39]V[43]Cr[43]Mn[46]Fe[46]Co[50]Ni[52]Cu[57]Zn[57]Ga[61]Ge[61]As[65]Se[67]Br[68]Kr[71]Rb[74]Sr[75]Y[79]Zr[81]Nb[83]Mo[86]Tc[88]Ru[90]Rh[94]Pd[94]Ag[94]Cd[97]In[100]Sn[100]Sb[104]Te[106]I[108]Xe[110]Cs[112]Ba[114]La[120]Ce[123]Pr[121]Nd[127]Pm[130]Sm[131]Eu[131]Gd[137]Tb[140]Dy[141]Ho[141]Er[145]Tm[146]Yb[151]Lu[150]Hf[154]Ta[156]W[158]Re[160]Os[162]Ir[165]Pt[168]Au[172]Hg[175]Tl[179]Pb[181]Bi[185]Po[190]At[193]Rn[196]Fr[200]Ra[202]Ac[206]Th[210]Pa[212]U[218]Np[225]Pu[228]Am[232]Cm[238]Bk[238]Cf[237]Es[241]Fm[242]Md[245]No[250]Lr[253]Rf[253]Db[255]Sg[258]Bh[261]Hs[264]Mt[266]
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