Concept explainers
Biodiversity Some biologists model the number of species S in a fixed area A (such as an island) by the species-area relationship
where c and k are positive constants that depend on the type of species and habitat.
- (a) Solve the equation for S.
- (b) Use part (a) to show that if k = 3, then doubling the area increases the number of species eightfold.
(a)
To solve: The equation for S in the equation
Answer to Problem 70E
The equation of S is
Explanation of Solution
Law used:
Let
Calculation:
Consider the equation,
Use the law of logarithm,
That is,
Take exponential function on both side of the equation (1).
Then, equation (1) becomes,
Therefore, the equation for S in the equation
(b)
To show: The count of species is 8 times to the initial count, when the area becomes double for
Explanation of Solution
Use the equation of part (a)
Represent the number of species in the area A for
Suppose the area increases 2 times for
Then, the no of species in the area 2A for
That is,
Compare the equations (1) and (2).
Thus, the number of species in the area 2A is 8 times the number of species in the area A for
Chapter 4 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- 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