area curve

(9:28:52 PM) PlanckWalk: Okay, so more like  y = a e^-(kx)
(9:30:41 PM) PlanckWalk: timeshifter: The relation f(x+1) = a e^(-k(x+1)) = a e^(-kx) e^-k = e^-k f(x)  gives you k = -ln(0.4)
(9:32:44 PM) PlanckWalk: mxms: It will hold for some choice fo a
(9:33:43 PM) timeshifter: ok so
(9:34:06 PM) timeshifter: if i plot y=e^-ln(0.4)x
(9:34:22 PM) timeshifter: that satisfies the f(x+1)=0.4*f(x)?
(9:34:37 PM) PlanckWalk: Yes
(9:34:42 PM) timeshifter: with you so far
(9:34:56 PM) PlanckWalk: Any constant multiple of that also satisfies it
(9:35:03 PM) timeshifter: which is a
(9:36:12 PM) PlanckWalk: The integral is  (-a/k) (e^(-12 k) - e^(-0 k)), i.e.  (a/k) (1 - e^(-12 k)) = 1000.  So  a = 1000 k / (1 - e^(-12 k))
(9:37:03 PM) timeshifter: man i wish i'd remembered more of my calculus class
(9:37:12 PM) PlanckWalk: timeshifter: e^(-12k) is really close to 0, so  a ~= 1000 k
(9:37:35 PM) timeshifter: and we know k, so that's just substitution
(9:37:39 PM) PlanckWalk: Yes
(9:38:11 PM) PlanckWalk: So numerically,  f(x) ~= 916.3 e^(-0.9163 x)