Concept explainers
Logistic Population Growth The table and scatter plot give the population of black flies in a closed laboratory container over an 18-day period.
- (a) Use the Logistic command on your calculator to find a logistic model for these data.
- (b) Use the model to estimate the time when there were 400 flies in the container.
Time (days) | Number of flies |
0 | 10 |
2 | 25 |
4 | 66 |
6 | 144 |
8 | 262 |
10 | 374 |
12 | 446 |
16 | 492 |
18 | 498 |
(a)
To find: The population logistic model for the data of the population of the black flies in a closed laboratory container over an 18-day period.
Answer to Problem 11P
The population logistic model that gives the best fits of the data point is
Explanation of Solution
Given:
The data is listed below in table by using the logistics command graphing calculator.
Times (days) | Number of flies |
0 | 10 |
2 | 25 |
4 | 66 |
6 | 144 |
8 | 262 |
10 | 374 |
12 | 446 |
16 | 492 |
18 | 498 |
Formula used:
A logistic growth model is a function of the form
Calculation:
Let us consider the variable
Use online graphing calculator and draw the logistic growth function of the form
From Figure 1, it is noticed that the logistic growth model
Therefore, The population logistic model that gives the best fits of the data point is
(b)
To estimate: The value of time when there are 400 flies in the container.
Answer to Problem 11P
The time when the number of flies in the container are 400 at
Explanation of Solution
From part (a) the number of flies
Here need to calculate the time, when the numbers of flies in the container are 400.
Substitute
Take
Thus, value of time when the number of flies in the container is
Therefore, the time when the number of flies in the container are 400 at
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