Question

A variable decays exponentially over time from an initial value $y_0$ toward zero according to $y=y_0\exp(-t/T)$ , where represents the time constant for the decay. At the moment when $t=T$ what is the relationship between and $y_0$ ?

_________ $y_0$

What is the relationship between and $y_0$ when ?

__________ $y_0$

How many time constants will have elapsed when ?

___________

Answer 1

at t = T

y = y_o exp (- T/T) = e^-1 y_o

at t = 6T

y = y_o exp (- 6T/T) = e^-6 y_o

y = y_o exp (- t/T)

y_o /9 = y_o exp (- t/T)

- 2.197 = -t/T

t = 2.197 T