What is the long term the number of fish?
a0 = 300 fish. decreases 15%, add 50. a1 = 95 a3 = 2.514 fish How can I find the long-term value (the limit)? Made for dummies, math flies right over my head …
I suppose that "decreases 15%, add 50 "is the rule for the number a (n +1) of fish in the next generation the number of fish (n) in the previous generation. A decrease of 15% means that 85% or 85/100 fraction remains: a (n +1) = (85/100) a (n) + 50. However, it can not make sense a1 = 95, a3 = 2514 fish. I get: a0 a1 = 300 = 305 = a2 = a3 309.25 312.8625 To find the limit (if any), give it a name: L. If a (e) becomes very close L, then so is a (n +1), so we will change both by L in the equation: L = (85/100) L + 50. Resolution of L gives L = 1000 / 3 = 333 333 …
Wrightsville Beach Fishing & Fly Tying, The Spoon Fly
