A breeding group of foxes is introduced into a protected area, and the population growth follows a logistic pattern. After t years, the population of foxes is given by the following. 43.5 foxes N = 0.25+0.76 (a) How many foxes were introduced into the protected area? (Round your answer to the nearest whole number.) Xfoxes (b) Make a graph of N versus t. 180 180 160 160 140 140 120 120 100 100 N 80 80 60 60 40 40 20- 20 0 5 20 15 25 5 15 20 10 25 t 180 180 160 160 140 140 120 120 100 100 N 80 80 60- 60 40 40 20 20 0 0 5 10 15 5 10 15 25 t Explain in words how the population of foxes increases with time. This answer has not been graded yet. (c) When will the fox population reach 100 individuals? (Round your answer to two decimal places.) The fox population will reach 100 individuals after years. Need Help? Read It Watch It Talk to a Tutor 25 20 20 10 N

A breeding group of foxes is introduced into a protected area, and the population growth follows a logistic pattern. After t years, the population of foxes is given by the following. 43.5 foxes N = 0.25+0.76 (a) How many foxes were introduced into the protected area? (Round your answer to the nearest whole number.) Xfoxes (b) Make a graph of N versus t. 180 180 160 160 140 140 120 120 100 100 N 80 80 60 60 40 40 20- 20 0 5 20 15 25 5 15 20 10 25 t 180 180 160 160 140 140 120 120 100 100 N 80 80 60- 60 40 40 20 20 0 0 5 10 15 5 10 15 25 t Explain in words how the population of foxes increases with time. This answer has not been graded yet. (c) When will the fox population reach 100 individuals? (Round your answer to two decimal places.) The fox population will reach 100 individuals after years. Need Help? Read It Watch It Talk to a Tutor 25 20 20 10 N

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Description: What are the blanks? A breeding group of foxes is introduced into a protected area, and the population growth follows a logistic pattern. After t years,the population of foxes is given by the following.43.5foxesN =0.25+0.76(a) How many foxes were int

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.4: Solving Nonlinear Equations

Problem 9E: A Population of Foxes A breeding group of foxes is introduced into a protected area, and the...

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Question

What are the blanks?

A breeding group of foxes is introduced into a protected area, and the population growth follows a logistic pattern. After t years,
the population of foxes is given by the following.
43.5
foxes
N =
0.25+0.76
(a) How many foxes were introduced into the protected area? (Round your answer to the nearest whole number.)
Xfoxes
(b) Make a graph of N versus t.
180
180
160
160
140
140
120
120
100
100
N
80
80
60
60
40
40
20-
20
0
5
20
15
25
5
15
20
10
25
t
180
180
160
160
140
140
120
120
100
100
N
80
80
60-
60
40
40
20
20
0
0
5
10
15
5
10
15
25
t
Explain in words how the population of foxes increases with time.
This answer has not been graded yet.
(c) When will the fox population reach 100 individuals? (Round your answer to two decimal places.)
The fox population will reach 100 individuals after
years.
Need Help?
Read It
Watch It
Talk to a Tutor
25
20
20
10
N

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More on the Pacific Sardine This is a continuation of Example 5.1. In this exercise, we explore the Pacific sardine population further, using the model in Example 5.1. a. If the current level of the Pacific sardine population is 50,000 tons, how long will it take for the population to recover to the optimum growth level of 1.2milliontons? Suggestion: One way to solve this is to make a new logistic formula using K2.4, r0.338, and N(0)0.05. b. The value of r used in Example 5.1 ignores the effects of fishing. If fishing mortality is taken into account, then r drops to 0.215 per year with the carrying capacity still at 2.4milliontons. Answer the question in part a using this lower value of r. Note: The population estimate of 50,000 tons and the adjusted value of r are given in the paper by Murphy see footnote 3 on page 347. Murphy points out that factoring in the growth of the competing anchovy population makes the recovery times even longer, and he adds. "It is disconcerting to realize how slowly the population will recover to its level of maximum productivity ... even if fishing stops." Studies to fit a logistic model to the Pacific sardine population have yielded. N=241+239e0.338t where t is measured in years and N is measured in millions of tons of fish. Part 1 What is r for the Pacific sardine? Part 2 According to the logistic model, in the absence of limiting factors, what would be the annual percentage growth rate for the Pacific sardine? Part 3 What is the environmental carrying capacity K? Part 4 What is the optimum yield level? Part 5 Make a graph of N versus t. Part 6 At what time t should the population he harvested? Part 7 What portion of the graph is concave up? What portion is concave down?
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Modeling Human Height with a Logistic Function A male child is 21inches long at birth and grows to an adult height of 73inches. In this exercise, we make a logistic model of his height as a function of age. a. Use the given information to find K and b for the logistic model. b. Suppose he reaches 95 of his adult height at age 16. Use this information and that from part a to find r. Suggestion: You will need to use either the crossing-graphs method or some algebra involving the logarithm. c. Make a logistic model for his height H, in inches, as a function of his age t, in years. d. According to the logistic model, at what age is he growing the fastest? e. Is your answer to part d consistent with your knowledge of how humans grow?
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A Population of Foxes A breeding group of foxes is introduced into a protected area, and the population growth follws a logistic pattern. After t years, the population of foxes is given by N=37.50.25+0.76t foxes. a. How many foxes were intorduced into the protected area? b. Make a graph of N versus t and explain in words how the populatoin of foxes increases with time. c. When will the fox population reach 100 individuals?