Concept explainers
To find: The value of
Answer to Problem 24E
The value of
The yeast will reach the population of 140 for the long run.
Explanation of Solution
Given:
The population is modelled by a function as below.
Differentiate (1) with respect to
At time
Increase rate of population with respect to time is given as below.
Calculation:
Equate the equation (4) and (2).
Substitute 0 for
Equate equation (4) and (3).
Determine the value of
Equate equation (4) and (5).
Substitute
The value cannot be negative.
Therefore, the value of
Determine the value of
Substitute 6 for
Therefore, the value of
Hence the value of
Determine the yeast population
For the population in long run take time
Hence the yeast will reach the population of 140 in the long run.
The value of
The yeast will reach the population of 140 for the long run.
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced 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