Suppose that in a logistic model the percentage growth rate G per year (in decimal form) as a function of N declines from G = 0.12 when N = 0 to G = 0 when N= 366. (a) What is the r value? r = (b) What is the carrying capacity? K = (c) At what value of N will there be a maximum growth rate? N = | Need Help? Read It

Suppose that in a logistic model the percentage growth rate G per year (in decimal form) as a function of N declines from G = 0.12 when N = 0 to G = 0 when N= 366. (a) What is the r value? r = (b) What is the carrying capacity? K = (c) At what value of N will there be a maximum growth rate? N = | Need Help? Read It

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: The growth of a population is modeled by a logistic equation, as shown in the graph below. What…

Q: 3. Since 1960, the growth in world population (in millions) closely fits the exponential function…

A: Given that, since 1960 the growth in world population (in millions) closely fits by the given…

Q: a. The table below shows some input-output pairs for an exponential function f. x 0 1 2 3 f(x) 51.2…

A: The exponential function is a mathematical function of the form ( f(x) = a^x ), where ( a ) is a…

Q: The table below shows the estimated value C, in dollars, of an 1877 Indian Head Cent (Philadelphia…

A: Consider the given exponential model Ct=29.490×1.076t. The above equation gives the growth factor…

Q: The curve appears to be levelling off at about __________ new cases by year, which indicates a limit…

A: a. The curve depicts a logistic growth model. b. The curve appears to be leveling off at about…

Q: A farm in Canada had 218 alpacas on January 1, 2004. After 8 years, the alpaca population decreases…

A: This question is based on exponential function.

Q: The logistic model P(t) = 95.4762 1+0.035240.1774t represents the percentage of households that do…

Q: Sin t = 3/5, cos t = 4/5 are given. Use identities to find tan t, csc t, sec t, and cot t. Where…

A: Given: sint=35, cost=45 we know that tanθ=sinθcosθcotθ=cosθsinθsecθ=1cosθcosecθ=1sinθ

Q: The current student population at a college is 8900 students. If enrollment is projected to increase…

A: Let's find.

Q: The demand for a 12-ounce bottle of sparkling water is given in the table. Demand Schedule for…

Q: A scientist is studying the number of bacteria that are growing in a culture in the biology lab.…

A: We have to find an exponential regression equation that can fit the given data. To find exponential…

Q: The following graph illustrates the population of bunnies, f(x), on a farm x years after 2000.…

A: Given: The points on the exponential function (1,12), (2, 18), (3,27)

Q: In 2002, a company sold 2,480 units. The company's accountant noticed a 5.2% continuous annual…

Q: A report tells us that in 2019 there were 800 of a certain type of animal in an area, but that the…

A: Question : A report tells us that in 2019 there were 800 of a certain type of animal in an area,…

Q: Exercise 4. Write the following functions in increasing order of growth (so f₁(n) = o(f₂(n)), etc.):…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

100%

Suppose that in a logistic model the percentage growth rate G per year (in decimal form) as a function of N declines from G = 0.12 when N = 0 to G = 0 when N= 366.
(a) What is the r value?
r =
(b) What is the carrying capacity?
K =
(c) At what value of N will there be a maximum growth rate?
N = |
Need Help?
Read It

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

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

Q8. Are rent rates influenced by the student population in a college town? Let rent be the average monthly rent paid on rental units in a college town in the United States. Let pop denote the total city population, avginc the average city income, and pctstu the student population as a percentage of the total population. One model to test for a relationship is log(rent) = 0.03048 + 0.5 * log(pop) +0.673 log(avginc) + 0.0046 pctstu (.844) (.039) (.081) (.0028) i) State the null hypothesis that the percentage of students relative to the population has no ceteris paribus effect on monthly rents. State the alternative that there is an effect. What signs do you expect for B₁ and ₂ ? The equation estimated for 64 college towns is log(rent) = 0.03048 + 0.5 * log(pop) + 0.673 log(avginc) + 0.0045 pctstu (.844) (.039) (.081) (.0017) Standard errors are given in the parentheses. test the null hypothesis H_0 that "10% ceteris paribus increase in population is associated with about a 6.6% increase…
Sexually Active Girls The percent of girls betweenages 15 and 20 who have been sexually active atsome time (the cumulative percent) can be modeledby the logistic functiony = 83.84/1 + 13.9233e-0.9248xwhere x is the number of years after age 15.a. Graph the function for 0 <= x <= 5.b. What does the model estimate the cumulativepercent to be for girls of age 16?c. What cumulative percent does the model estimatefor girls of age 20?d. What is the upper limit implied by the givenlogistic model?
A new car costs $27, 000 depreciates to 80% of its value in 2 years. Round all answers to 2 decimal places, where necessary. a. Assume that the depreciation is linear. What is the linear function that models the value of this car t years after purchase? f(t) = Preview b. Assume that the value of the car is given by an exponential function Aekt, where A is the initial price of the car. Find the value of the constant k. Answer exactly. k = Preview c. For the linear model used in part (a), find the value of the car 6 years after the purchase, then do the same for the exponential model used in part (b). Round your answer to 2 decimal places. Linear after 6 years: $ Exponential after 6 years: $
17 sc
A certain quantity has a yearly growth factor of 1.12. What is its monthly growth factor? (Round your answer to two decimal places.)
The table below shows some input-output pairs for an exponential function g. > i. Determine the 1-unit scale (growth/decay) factor for g. Preview ii. Determine the 1-unit percent g (i.e., express the scale factor as a percent). iii. Determine the 1-unit percent change for g. Preview g(x) = iv. Determine the initial value for g (the output value when the input is 0.) g(0) = = v. Write a function formula for 9. X 2 1 g(x) 26.64 31.968 Preview Preview
1. Company A has 100 stores and adds 50 new stores per year. Company B has 100 stores and increases the number of stores by 50% per year. a. Write a function representing the growth of Company B. b. How many stores will Company B have after 4 years assuming the same growth rate? Show your work.
a. Consider the exponential function ƒ(x) = 54(0.38)ª. i. What is the initial value of f? f(0) = 54 ii. What is the 1-unit growth factor for f? 0.38 Preview % Preview iii. What is the 1-unit percent change for f? Preview
Nitrogen dioxide, NO2, is an air pollutant resulting from burning fossil fuels in cars and power plants. The following table shows the decrease in the national average of the concentration in parts per billion (ppb) of NO2 for selected years. Year 2014 2015 2016 2017 2018 NO2 (ppb) 40.8107 39.7886 38.7972 37.8209 36.8752 Use exponential regression to find an exponential decay function for the concentration, C, of NO2 t years after 2014. Round constants to the nearest ten-thousandth. C = Use the model to predict the concentration of NO2 (in ppb) in 2050. Round to the nearest whole number. ? ppb
A client’s orders are growing consistently at x% per year. A) If three years from now orders are 50% higher than today, what is the annual growth rate (x)? B) Write an expression (in terms of x) for how many years it will take until orders are double what they are currently
The logistic model P(t) = 96.0235 1+0.0455-0.1864t represents the percentage of households that do not own a personal computer t years since 1983. Complete parts (a)-(d). (a) Evaluate and interpret P(0). Evaluate P(0). P(0) = 91.8 % (Round to one decimal place as needed.) Which sentence below best describes P(0)? O A. P(0) is the year all households had a personal computer. O B. O C. O D. P(0) is the year no households had a personal computer. P(0) is the percentage of households with a personal computer in 1983. P(0) is the percentage of households without a personal computer in 1983. -C
One of the possible models for the coronavirus is the logistic curve, shown here without scale. This curve shows the total number of cases of people infected with the virus. The rate of change for this curve is the number of ca es per day. 1. On the curve, mark the point at which the number of cases per day is greatest. What is a mathematical term for this point? 2. One of the criteria for re-opening activities is fourteen consecutive da s with a decreasing number of cases. Where is this on the curve? Number of Infected people as a function of time