Give the formulas for finding the growth rate (r) and the carrying capacity (N). • r = ? • N = ? WK Topic 13COLA thingscalstatela instructure.com/courses/78782/assignments/1268237Important My Personal thingsQuestion 3N = Select an answerW2022 Class websites Getting Started - Da...SRecall that the logistic model can be written in the form#ea) Give the formulas for finding the growth rater and the carrying capacity N.r = Select an answerC$r%<5t8 Stoneridge Manage...>gPn = b.Pn-1-a. P²-1Your Shopping Cart...h1u10IO111GR 361- Oct 27111₁

We have to find carrying capacity and growth rate, by comparing the logistics model formula to the…

Recall that the logistic model can be written in the form a) Give the formulas for finding the growth rate r and the carrying capacity N. r = Select an answer Pn = b.Pn-1-a. P²-1 N = Select an answer ✓

Recall that the logistic model can be written in the form a) Give the formulas for finding the growth rate r and the carrying capacity N. r = Select an answer Pn = b.Pn-1-a. P²-1 N = Select an answer ✓

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

Chapter5: A Survey Of Other Common Functions

Section5.1: Logistic Functions

Problem 2SBE: SKILL BUILDING EXERCISES Estimating Carrying Capacity In Figure 5.17, a portion of the logistic...

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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.
Long-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?
What situations are best modeled by a logistic equation? Give an example, and state a case for why the example is a good fit.
Cable 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?
Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time moved on. Table 4 shows the number of games sold, in thousands, from the years 20002010. a. Let x represent time in years starting with x=1 for the year 2000. Let y represent the number of games sold in thousands. Use logarithmic regression to fit a model to these data. b. If games continue to sell at this rate, how many games will sell in 2015? Round to the nearest thousand.
What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
SKILL BUILDING EXERCISES Estimating Optimum Yield In Figure 5.16, a logistic growth curve is sketched. Estimate the optimum yield level and the time when this population should be harvested. FIGURE 5.16 A logistic growth curve
Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?
SKILL BUILDING EXERCISES Estimating Carrying Capacity In Figure 5.17, a portion of the logistic growth curve is sketched. Estimate the optimum yield level and the carrying capacity. FIGURE 5.17 A portion of the logistic growth curve
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?