The problem with your math is that your r(t) isn’t the same as my r. If v(Deltat ) gives the factor by which you discount a future resource acquisition that will occur Deltat in the future, then r is for people who have a v(Deltat ) of the form
v(Deltat = \frac{1}{r}^{\Delta%20t})
Your equation is for people who have a
where k is some constant.
vDelta
The problem with your math is that your r(t) isn’t the same as my r. If v(Deltat ) gives the factor by which you discount a future resource acquisition that will occur Deltat in the future, then r is for people who have a v(Deltat ) of the form
v(Deltat = \frac{1}{r}^{\Delta%20t})
Your equation is for people who have a
where k is some constant.
vDelta