Calculus For The Life Sciences
2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: Pearson Addison Wesley,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 14.CR, Problem 4CR
To determine
Whether the statement “the value
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A field currently contains 20 mint plants. Absent constraints, the number of plants would increase by 30%
each year, but the field can only support a maximum population of 100 plants. Use the logistic model to
predict the population in the next two years. Round answers to 1 decimal place.
P1 =
P₂ =
a scuba diver used her camera equipment to measure the intensity of light, in lux, as she dove into the lake. She compared her readings with the depth of water at each point.
light intensity(lux) - 5.0, 4.0, 3.0, 2.0, 1.0
depth of water(m) - 2.3, 3.1, 4.0, 5.4, 7.7
(a) use logarithmic regression to model data, round all values to the nearest hundredth
(b) At what depth, to the nearest tenth of a metre is the light intensity 3.6 lux
(c) What is the light intensity at the surface, round to the nearest tenth
Biologists stocked a lake with 80 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 2,000. The number of fish tripled in the first year.
(a) Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years.
P =
(b) How long will it take for the population to increase to 1000? (Round your answer to two decimal places.)
yr
Chapter 14 Solutions
Calculus For The Life Sciences
Ch. 14.1 - YOUR TURN 1 Find the first four terms of the...Ch. 14.1 - Prob. 2YTCh. 14.1 - Prob. 3YTCh. 14.1 - Prob. 4YTCh. 14.1 - Prob. 1ECh. 14.1 - Prob. 2ECh. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Prob. 5ECh. 14.1 - Prob. 6E
Ch. 14.1 - Prob. 7ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - Prob. 10ECh. 14.1 - Prob. 11ECh. 14.1 - Prob. 12ECh. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.1 - Prob. 16ECh. 14.1 - Prob. 17ECh. 14.1 - Prob. 18ECh. 14.1 - Prob. 19ECh. 14.1 - Prob. 20ECh. 14.1 - Prob. 21ECh. 14.1 - Prob. 22ECh. 14.1 - Prob. 23ECh. 14.1 - Prob. 24ECh. 14.1 - Ricker Model Another model of population growth...Ch. 14.1 - Prob. 26ECh. 14.1 - Prob. 27ECh. 14.1 - Beverton-Holt Model Another model of population...Ch. 14.1 - Prob. 29ECh. 14.1 - Prob. 30ECh. 14.1 - Shepherd Model The Shepherd model, a modification...Ch. 14.1 - Prob. 32ECh. 14.1 - Prob. 33ECh. 14.2 - Find equilibrium points x, 0x1, for each of the...Ch. 14.2 - Prob. 2ECh. 14.2 - Prob. 3ECh. 14.2 - Prob. 4ECh. 14.2 - Prob. 5ECh. 14.2 - Prob. 6ECh. 14.2 - Prob. 7ECh. 14.2 - Prob. 8ECh. 14.2 - Prob. 9ECh. 14.2 - Prob. 10ECh. 14.2 - Prob. 11ECh. 14.2 - Prob. 12ECh. 14.2 - Prob. 13ECh. 14.2 - Prob. 14ECh. 14.2 - For each of the following functions, already...Ch. 14.2 - Prob. 17ECh. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.2 - Prob. 20ECh. 14.2 - Prob. 21ECh. 14.3 - Prob. 1YTCh. 14.3 - Prob. 1ECh. 14.3 - Prob. 2ECh. 14.3 - Prob. 3ECh. 14.3 - Prob. 4ECh. 14.3 - Prob. 5ECh. 14.3 - Prob. 6ECh. 14.3 - Prob. 11ECh. 14.3 - Prob. 12ECh. 14.3 - Repeat the instruction of Exercise 11 for the...Ch. 14.3 - Prob. 14ECh. 14.3 - Prob. 15ECh. 14.3 - Prob. 16ECh. 14.3 - Prob. 17ECh. 14.3 - Prob. 18ECh. 14.3 - Prob. 19ECh. 14.CR - CONCEPT CHECK For Exercise 1-8 determine whether...Ch. 14.CR - Prob. 2CRCh. 14.CR - Prob. 3CRCh. 14.CR - Prob. 4CRCh. 14.CR - Prob. 5CRCh. 14.CR - Prob. 6CRCh. 14.CR - Prob. 7CRCh. 14.CR - Prob. 8CRCh. 14.CR - Prob. 9CRCh. 14.CR - Prob. 10CRCh. 14.CR - Prob. 11CRCh. 14.CR - Prob. 12CRCh. 14.CR - Find the next 4 terms of the sequence satisfying...Ch. 14.CR - Prob. 14CRCh. 14.CR - Prob. 15CRCh. 14.CR - Prob. 16CRCh. 14.CR - Prob. 17CRCh. 14.CR - Prob. 18CRCh. 14.CR - Prob. 19CRCh. 14.CR - Prob. 20CRCh. 14.CR - Prob. 21CRCh. 14.CR - Prob. 22CRCh. 14.CR - Prob. 23CRCh. 14.CR - Prob. 24CRCh. 14.CR - For each of the following functions, do the...Ch. 14.CR - Prob. 26CR
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Does a linear, exponential, or logarithmic model best fit the data in Table 2? Find the model.arrow_forwardWhat 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?arrow_forwardThe population of a culture of bacteria is modeled by the logistic equation P(t)=14,2501+29e0.62t where t is inarrow_forward
- World Population The following table shows world population N, in billions, in the given year. Year 1950 1960 1970 1980 1990 2000 2010 N 2.56 3.04 3.71 4.45 5.29 6.09 6.85 a. Use regression to find a logistic model for world population. b. What r value do these data yield for humans on planet Earth? c. According to the logistic model using these data, what is the carrying capacity of planet Earth for humans? d. According to this model, when will world population reach 90 of carrying capacity? Round to the nearest year. Note: This represents a rather naive analysis of world population.arrow_forwardBuffalo: Waterton Lakes National Park of Canada, where the Great Plains dramatically meet the Rocky Mountains in Alberta, has a migratory buffalo bison herd that spends falls and winters in the park. The herd is currently managed and so kept small; however, if it were unmanaged and allowed to grow, then the number N of buffalo in the herd could be estimated by the logistic formula N=3151+14e0.23t Here t is the number of years since the beginning of 2002, the first year the herd is unmanaged. a. Make a graph of N versus t covering the next 30 years of the herds existance corresponding to dates up to 2032. b. How many buffalo are in the herd at the beginning of 2002? c. When will the number of buffalo first exceed 300?. d. How many buffalo will there eventually be in the herd? e. When is the graph of N, as a function of t, concave up? When is it concave down? What does this mean in terms of the growth of the buffalo herd?.arrow_forwardCable TV The following table shows the number C. in millions, of basic subscribers to cable TV in the indicated year These data are from the Statistical Abstract of the United States. Year 1975 1980 1985 1990 1995 2000 C 9.8 17.5 35.4 50.5 60.6 60.6 a. Use regression to find a logistic model for these data. b. By what annual percentage would you expect the number of cable subscribers to grow in the absence of limiting factors? c. The estimated number of subscribers in 2005 was 65.3million. What light does this shed on the model you found in part a?arrow_forward
- Eastern Pacific Yellowfin Tuna Studies to fit a logistic model to the Eastern Pacific yellowfin tuna population have yielded N=1481+36e2.61t where t is measured in years and N is measured in thousands of tons of fish. a. What is the r value for the Eastern Pacific yellowfin tuna? b. What is the carrying capacity K for the Eastern Pacific yellowfin tuna? c. What is the optimum yield level? d. Use your calculator to graph N versus t. e. At what time was the population growing the most rapidly?arrow_forwardEnter the data from Table 2 into a graphing calculator and graph the ranking scatter plot. Determine whetherthe data from the table would likely represent a function that is linear, exponential, or logarithmic.arrow_forwardThe population of a lake of fish is modeled by the logistic equation P(t)=16,1201+25e0.75t, where t is time inyears. To the unrest hundredth, how manyyears will it take the lake to reach 80% of its carrying capacity?For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table.Observe the shape of the scatter diagram to determine whether the data is best described by an exponential,logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models thedata. When necessary, round values to five decimal places.arrow_forward
- Please answer fast a population of 400 African zebra exhibits logistic growth. If maximum number of zebras in the population is 1600 zebras and over the year there has been 30 births and 10 deaths and no immigration or emigration. What is the population growth rate for the population? a. 6 individuals/year b. 10 individuals/year c. 12 individuals/year d. 15 individuals/yeararrow_forwardA conservation organization releases 35 Florida panthers into a game preserve. After 4 years, there are 178 panthers in the preserve. The Florida preserve has a carrying capacity of 420 panthers. (a) Write a logistic equation that models the population of panthers in the preserve. (Round your k to four decimal places. Use t for the time in years.) P = (b) Find the population after 5 years. (Round your answer to the nearest whole number.) 233 panthers 420 1+11e-0.5227t (c) When will the population reach 210? (Round your answer to two decimal places.) 4.59 yr (d) Write a logistic differential equation that models the growth rate of the panther population. Then using Euler's Method, repeat part (b) with a step size of h = 1. Use the initial release population of 35 panthers as your initial value to start Euler's Method. (Round your answer to the nearest whole number.) 0.5227P 1 dP dt = P(5) 195 X P 420 (e) At what time is the panther population growing most rapidly? (Round your answer to…arrow_forwardA rumor is spreading on an island with a population of 50,000 individuals. When the rumor starts to spread, 100 individuals heard it, and 4 days later, 250 people have heard the rumor. Assuming that the number of people that have heard the rumor is growing according to the logistic model, how many individuals will have heard the rumor 20 days after it started to spread?arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY