The relative growth rate r of a function f measures the change in the function compared to its value at a particular point. It is computed as r(t) = TAT A logistic growth model for a certain population with a base population of 5 individuals, carrying capacity of 12individuals, and a base growth rate of 0.025 is shown below. Complete parts (a) through (c).60P(t) =5 +7e -0.025tP'(0)a. Is the relative growth in 1999 (t= 0) for the logistic model of the above population equal to r(0) == 0.015 (rounding to three decimal places)? This would mean that the population was growing at 1.5% per year.P(0)YesNob. Compute the relative growth rate of the population in 2005 and 2030. What appears to be happening to the relative growth rates as time increases?r(6) =r(31) =|(Round to four decimal places as needed.)What appears to be happening to the relative growth rates as time increases?O A. As time increases, the rate of population growth decreases.O B. As time increases, the rate of population growth increases.OC. As time increases, the rate of population growth nears the carrying capacity.O D. As time increases, the rate of population growth nears the initial population. P'(t)c. Evaluate lim r(t) = limP(t)where P(t) is the logistic growth function from above. What does your answer say about populations that follow a logistic growth pattern?t00t00lim r(t) =t00(Simplify your answer.)Choose the correct answer below.O A. As the population gets close to carrying capacity, the rate of population growth increases.O B. As the population gets close to carrying capacity, the rate of population growth vanishes.O C. As the population gets close to the initial population, the rate of population growth vanishes.O D. As the population gets close to carrying capacity, the rate of population growth equals the carrying capacity.

The relative growth rate r of a function f measures the change in the function compared to its value at a particular point. It is computed as r(1) = 7 A logistic growth model for a certain population with a base population of 5 individuals, carrying capacity individuals, and a base growth rate of 0.025 is shown below. Complete parts (a) through (c). 60 P(t) = 5+7e -0.025 P'(0) a. Is the relative growth in 1999 (t= 0) for the logistic model of the above population equal to r(0) = DVO = 0.015 (rounding to three decimal places)? This would mean that the population was growing at 1.5% per year. Yes O No b. Compute the relative growth rate of the population in 2005 and 2030. What appears to be happening to the relative growth rates as time increases? r(6) =O r(31) = (Round to four decimal places as needed.) What appears to be happening to the relative growth rates as time increases? O A. As time increases, the rate population growth decreases. O B. As time increases, the rate population growth increases. O C. As time increases, the rate of population growth nears the carrying capacity.

The relative growth rate r of a function f measures the change in the function compared to its value at a particular point. It is computed as r(1) = 7 A logistic growth model for a certain population with a base population of 5 individuals, carrying capacity individuals, and a base growth rate of 0.025 is shown below. Complete parts (a) through (c). 60 P(t) = 5+7e -0.025 P'(0) a. Is the relative growth in 1999 (t= 0) for the logistic model of the above population equal to r(0) = DVO = 0.015 (rounding to three decimal places)? This would mean that the population was growing at 1.5% per year. Yes O No b. Compute the relative growth rate of the population in 2005 and 2030. What appears to be happening to the relative growth rates as time increases? r(6) =O r(31) = (Round to four decimal places as needed.) What appears to be happening to the relative growth rates as time increases? O A. As time increases, the rate population growth decreases. O B. As time increases, the rate population growth increases. O C. As time increases, the rate of population growth nears the carrying capacity.

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...

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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

The relative growth rate r of a function f measures the change in the function compared to its value at a particular point. It is computed as r(t) = TAT A logistic growth model for a certain population with a base population of 5 individuals, carrying capacity of 12
individuals, and a base growth rate of 0.025 is shown below. Complete parts (a) through (c).
60
P(t) =
5 +7e -0.025t
P'(0)
a. Is the relative growth in 1999 (t= 0) for the logistic model of the above population equal to r(0) =
= 0.015 (rounding to three decimal places)? This would mean that the population was growing at 1.5% per year.
P(0)
Yes
No
b. Compute the relative growth rate of the population in 2005 and 2030. What appears to be happening to the relative growth rates as time increases?
r(6) =
r(31) =|
(Round to four decimal places as needed.)
What appears to be happening to the relative growth rates as time increases?
O A. As time increases, the rate of population growth decreases.
O B. As time increases, the rate of population growth increases.
OC. As time increases, the rate of population growth nears the carrying capacity.
O D. As time increases, the rate of population growth nears the initial population.

P'(t)
c. Evaluate lim r(t) = lim
P(t)
where P(t) is the logistic growth function from above. What does your answer say about populations that follow a logistic growth pattern?
t00
t00
lim r(t) =
t00
(Simplify your answer.)
Choose the correct answer below.
O A. As the population gets close to carrying capacity, the rate of population growth increases.
O B. As the population gets close to carrying capacity, the rate of population growth vanishes.
O C. As the population gets close to the initial population, the rate of population growth vanishes.
O D. As the population gets close to carrying capacity, the rate of population growth equals the carrying capacity.

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