A model for the number of lobsters caught per year is based on the assumption that the number of lobsters caught in a year is the average of the number caught in the two previous years.
(a) Find a recurrence relation for {Pn}, where Pn is the number of lobsters caught in year n, under the assumption for this model.
(b) Find Pn if 100000 lobsters were caught in year 1 and 300000 were caught in year 2.
Hello, bhuvan!
I know some techniques for this problem.
I hope they're appropriate for your course.
A model for the number of lobsters caught per year is based on the assumption
that the number of lobsters caught in a year is the average of the number
caught in the two previous years.
(a) Find a recurrence relation for , the number of lobsters caught in year
. .
(b) Find if
From (a), we have: . .[1]
We conjecture that is an exponential function: .
Then [1] becomes: .
. . Divide by
. . And we have two roots: .
Then: .
Form a linear combination of these roots:
. .
We know the first two values of this sequence:
. .
Subtract [2] from [3]: .
Substitute into [3]: .
Therefore: .
Thanks you very much !!
Do you know how to solve below problem i am trying to solve this but i am confuse..
Consider the non homogeneous linear recurrence relation an=2an-1+2^n
(a) show that an=n2^n is a solution of this relation.
i tried to solve this by putting an value in
2an-1+2^n=2(n2^n)+2^n)=2^n(2n+1) but i am not getting right answer as far as i think.