Question

Suppose that a small library has an inventory of books Bn, where Bn is the number of books the nth year. Due to wear and tear and lost books, the library loses 10% of its books every year. However, with library fines the library is able to purchase 50 books a year.

a. Write down a dynamical system describing the number of books per year. Assume an unspecified initial condition B0=B0.

b. What is the long-term behavior (fixed point) for the number of books over time?

2. In a hypothetical scenario, hawks have recently expanded their territory to overlap with that of the owls in a national park. Due to the migration of the hawks from a larger region, the population of hawks in the park increases steadily by 50 hawks a year. The hawks are not negatively affected by the owls and do not appear to be nesting in the park, so that their population is not growing other than the steady migration. Before the arrival of the hawks, the owls had a positive birth rate described by ?1 = 0.2. The activists estimate that the negative affect of the hawks on the owls is ?3 = 0.001. Write down a dynamical system describing this scenario for the number of owls Wn and hawks Hn in the park over time.

Answer 1

1) a)

That is is the dynamical system with is the initial amount

Fixed point is means is the final stable number of books

2) is the required dynamical system

Hope this was helpful. Please do leave a positive rating if you liked this answer. Thanks and have a good day!