Concept explainers
Let c be a positive number. A differential equation of the form
where k is a positive constant, is called a doomsday equation because the exponent in the expression ky1 +c is larger than the exponent 1 for natural growth.
(a) Determine the solution that satisfies the initial condition y(0) = y0.
(b) Show that there is a finite time t = T (doomsday) such that
(c) An especially prolific breed of rabbits has the growth term ky1.01. If 2 such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?
Trending nowThis is a popular solution!
Chapter 9 Solutions
Calculus: Early Transcendentals
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning