is there an exponential decay formula ?

Question

Using an exponential best-fit model, after how many years is the car valued at half of the original value

Answer 1

many thangs go as x=xstart*e^-kt, t=time yunit such as yeers

Yu need tu dind a value for k for wotever yu werk with

A nu kar in US drop tu half its nu value in bout 3 yeers

kall this the "half life"

If yuze equashun, x/xstart=e^-it & evaluate it at 3 yeer=1/2, yu get

e^-3k=0.5

take ln & yu get -3k=ln(0.5)

or k=-(1/3)ln(0.5)

ln(0.5)=-0.6931471805599453

so k=+0.23104906018665