Let the population be a time , at time and at time . Using this notation, you know how to write the increase in population from time to , don't you?
I know how to solve Recurrence Relation problems, I just need help writing up the equation:
Assume that the deer population of Rustic County is 200 at timen = 0 and 220 at time n = 1 and that the increase from time n-1 to time n is twice the increase from time n-2 to time n-1. Write a recurrence relation and an initial condition that de ne the deer population at time n and then solve the recurrence relation.
Hello, aamiri!
Assume that the deer population of Rustic County is 200 at time 0,
and 220 at time 1.
And that the increase from time to time is twice the increase
from time to time
(a) Write a recurrence relation and an initial condition
that define the deer population at time
(b) Solve the recurrence relation.
Let = deer population at time
We are given: .
We are told that: .
. . . . . . . . . . . . .
. . . . . . . . . . . . .
. . . . . . . . . . . . . .(a)
Hence: .
Let
Divide by
. . Hence: .
The function is of the form: .
We know the first two terms of the sequence:
Subtract [2] - [1]: .
Substitute into [1]: .
Therefore: . (b)