Calculus For The Life Sciences
2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: Pearson Addison Wesley,
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Chapter 14.CR, Problem 6CR
To determine
Whether the statement “for the logistic equation, there is always at least one stable equilibrium point” is true or false
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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
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- 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_forwardLong-Term Data and the Carrying Capacity This is a continuation of Exercise 13. Ideally, logistic data grow toward the carrying capacity but never go beyond this limiting value. The following table shows additional data on paramecium cells. t 12 13 14 15 16 17 18 19 20 N 610 513 593 557 560 522 565 517 500 a. Add these data to the graph in part b of Exercise 13. b. Comment on the relationship of the data to the carrying capacity. Paramecium Cells The following table is adapted from a paramecium culture experiment conducted by Cause in 1934. The data show the paramecium population N as a function of time t in days. T 2 3 5 6 8 9 10 11 N 14 34 94 189 330 416 507 580 a. Use regression to find a logistic model for this population. b. Make a graph of the model you found in part a. c. According to the model you made in part a, when would the population reach 450?arrow_forwardExercise 3. This problem is a modeling discussion around one parameter. The model below represents a predator-prey model. Let’s say R represents rabbits and F are the foxes. The way we model the equations we see that the rabbits, in the absence of foxes, follow a logistic equation and stabilize at a population of 100. On the other hand, without rabbits, the foxes follow a decaying exponential and go extinct to model the fact that they are dependent on the prey for their survival. The predation terms −5RF and 2RF have obviously similar forms as in an epidemic but they are not equal since the first represent predator efficiency (the number of rabbits killed) and the sec- ond represents food intake (the growth due to feeding in the fox population). α represents a harvesting (hunting) effect. We assume that the harvesting happens at the SAME rate α. R′ =(100−R)R−5RF −αR, F ′ = 2RF − 20F − αF. (a) Find the NON-ZERO equilibrium point (the one in which both R and F are non-zero, also…arrow_forward
- Please please answer both a and b Thank you so mucharrow_forwardPlease 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_forwardLorna knows that the species of fish in her pond is modeled by a logistic population model with a relative growth rate of 0.4 per year. Sergio, her husband, notes that the carrying capacity of the pond is 15 000. If at the start, the pond has 500 fishes, How many fishes will there be after 5 years? a. 3044 b. 3045 c. 3046 d. 3047arrow_forward
- Suppose that a population follows a logistic growth model. The population in the first year is 21.7 thousand. In the second year the population has increased by 54 hundred. In the third year, the population has increased by 17 hundred. Find the carrying capacity of the population.arrow_forwardCensus data for the United States between1790 and 1950 are given in Table. Construct a logisticpopulation model using the data from 1790, 1850, and 1910.(b) Construct a table comparing actual census populationwith the population predicted by the model in part (a).Compute the error and the percentage error for each entrypair.arrow_forwardAssume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1400 fish. Absent constraints, the population would grow by 210% per year.If the starting population is given by p0=200p0=200, then after one breeding season the population of the pond is given byp1p1 = After two breeding seasons the population of the pond is given byp2p2 =arrow_forward
- Please see attached picturearrow_forwardThe trout population in Lake Beautiful is growing according to the logistic model, P(t) = 1+ ae-bt where P(t) is the number of trout (measured in thousands) years after 2015. The carrying capacity of the lake is 12,000 trout, in 2015 there were 6,000 trout in the lake, and by 2020 the trout population had reached 8,000. Find the numbers a, b and C and use this model to predict Lake Beautiful's trout population in 2023. Round your answer to the nearest hundred.arrow_forwarda 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 tentharrow_forward
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