A nation's population (to the nearest million) was 281 million in 2000 and 311 in 2010. It is projected that the population in 2050 will be 439 million. To construct a logistic model, both the growth rate and the carrying capacity must be estimated. There are several ways to estimate these parameters. Use parts (a) through (f) to us one approach. a. Assume that t= 0 corresponds to 2000 and that the population growth is exponential for the first ten years; that is, between 2000 and 2010, the population is given by P(t) = P(0) e". Estimate the growth rate r using this assumption. r=(Round to five decimal places as needed.) b. Write the solution of the logistic equation with the value of r found in part (a). Write any populations in the logistic equation in millions of people. P(t) = Use the projected value P(50) = 439 million to find a value of the carrying capacity K. K=(Type an integer or decimal rounded to the nearest hundredth as needed.) c. According to the logistic model determined in parts (a) and (b), when will the country's population reach 95% carrying capacity? The population will reach 95% of the carrying capacity in the year (Type an integer or decimal rounded to the nearest hundredth as needed.)

A nation's population (to the nearest million) was 281 million in 2000 and 311 in 2010. It is projected that the population in 2050 will be 439 million. To construct a logistic model, both the growth rate and the carrying capacity must be estimated. There are several ways to estimate these parameters. Use parts (a) through (f) to us one approach. a. Assume that t= 0 corresponds to 2000 and that the population growth is exponential for the first ten years; that is, between 2000 and 2010, the population is given by P(t) = P(0) e". Estimate the growth rate r using this assumption. r=(Round to five decimal places as needed.) b. Write the solution of the logistic equation with the value of r found in part (a). Write any populations in the logistic equation in millions of people. P(t) = Use the projected value P(50) = 439 million to find a value of the carrying capacity K. K=(Type an integer or decimal rounded to the nearest hundredth as needed.) c. According to the logistic model determined in parts (a) and (b), when will the country's population reach 95% carrying capacity? The population will reach 95% of the carrying capacity in the year (Type an integer or decimal rounded to the nearest hundredth as needed.)

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Description: A nation's population (to the nearest million) was 281 million in 2000 and 311 in 2010. It is projected that the population in 2050 will be 439 million. To construct alogistic model, both the growth rate and the carrying capacity must be estimated.

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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Question

A nation's population (to the nearest million) was 281 million in 2000 and 311 in 2010. It is projected that the population in 2050 will be 439 million. To construct a
logistic model, both the growth rate and the carrying capacity must be estimated. There are several ways to estimate these parameters. Use parts (a) through (f) to use
one approach.
a. Assume that t = 0 corresponds to 2000 and that the population growth is exponential for the first ten years; that is, between 2000 and 2010, the population is given
by P(t) = P(0) e". Estimate the growth rate r using this assumption.
= (Round to five decimal places as needed.)
b. Write the solution of the logistic equation with the value of r found in part (a). Write any populations in the logistic equation in millions of people.
P(t) =
Use the projected value P(50) = 439 million to find a value of the carrying capacity K.
K= (Type an integer or decimal rounded to the nearest hundredth as needed.)
c. According to the logistic model determined in parts (a) and (b), when will the country's population reach 95% carrying capacity?
The population will reach 95% of the carrying capacity in the year
(Type an integer or decimal rounded to the nearest hundredth as needed.)

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