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 following. 38.5 N = foxes 0.22 + 0.76 (a) How many foxes were introduced into the protected area? (Round your answer to the nearest whole number.) foxes (b) Make a graph of N versus t. 180 180 160 160 140 140 120 120 100 100 80 80 60 60 40 40 20 20 10 15 20 25 10 15 20 25 180 180 160 160 140 140 120 120 100 100 80 60 60 40 40 20 20 10 15 20 10 15 20 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 75 individuals? (Round your answer to two decimal places.) The fox population will reach 75 individuals after years.

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 following. 38.5 N = foxes 0.22 + 0.76 (a) How many foxes were introduced into the protected area? (Round your answer to the nearest whole number.) foxes (b) Make a graph of N versus t. 180 180 160 160 140 140 120 120 100 100 80 80 60 60 40 40 20 20 10 15 20 25 10 15 20 25 180 180 160 160 140 140 120 120 100 100 80 60 60 40 40 20 20 10 15 20 10 15 20 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 75 individuals? (Round your answer to two decimal places.) The fox population will reach 75 individuals after years.

Name: 3 A breeding group of foxes is introduced into a protected area, and t
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Description: 3 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 thefollowing.38.5N =foxes0.22 + 0.76(a) How many foxes were introduced into the

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 15DE

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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?
The fox population in a certain region has an annualgrowth rate of 9 per year. In the year 2012, therewere 23,900 fox counted in the area. What is the foxpopulation predicted to be in the year 2020 ?
What is the y -intercept of the logistic growth model y=c1+aerx ? Show the steps for calculation. What does this point tell us about the population?
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What situations are best modeled by a logistic equation? Give an example, and state a case for why the example is a good fit.
Use a graphing calculator to solve each problem. In Example 4, suppose that a birth control program changed the formula for poulation growth to Pt=1000e0.01t. How long will the food supply be adequate? EXAMPLE 4 Using a Graphing Calculator to Solve a popuiation Problem Suppose that a country with a population of 1000 people is growing exponentially according to the population function Pt=1000e0.02t Where t in years. Furthermore, assume that the food supply, measured in adequate food per day per person, is growing linearly according to the function fx=30.625x+2000 In how many years will the population outstrip the food supply?
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?