Suppose the population of the world was about 6.2 billion in 2000. Birth rates around that time ranged from 35 to 40 million per year and death rates ranged from 15 to 20 million per year. Let's assume that the carrying capacity for world population is 20 billion. (a) Write the logistic differential equation for these data. (Because the initial population is small compared to the carrying capacity, you can take k to be an estimate of the initial relative growth rate. Calculate k using the maximum birth rate and maximum death rate. Let t = 0 correspond to the year 2000.) dP dt = (b) Use the logistic model to estimate the world population (in billions) in the year 2010. (Round your answer to the nearest hundredth.) billion. Compare this result with the actual population of 6.9 billion. This result ---Select--- the actual population of 6.9 billion. OUR TEACHER (c) Use the logistic model to predict the world population (in billions) in the years 2100 and 2500. (Round your answers to the nearest hundredth.) 2100 2500 billion billion:
Suppose the population of the world was about 6.2 billion in 2000. Birth rates around that time ranged from 35 to 40 million per year and death rates ranged from 15 to 20 million per year. Let's assume that the carrying capacity for world population is 20 billion. (a) Write the logistic differential equation for these data. (Because the initial population is small compared to the carrying capacity, you can take k to be an estimate of the initial relative growth rate. Calculate k using the maximum birth rate and maximum death rate. Let t = 0 correspond to the year 2000.) dP dt = (b) Use the logistic model to estimate the world population (in billions) in the year 2010. (Round your answer to the nearest hundredth.) billion. Compare this result with the actual population of 6.9 billion. This result ---Select--- the actual population of 6.9 billion. OUR TEACHER (c) Use the logistic model to predict the world population (in billions) in the years 2100 and 2500. (Round your answers to the nearest hundredth.) 2100 2500 billion billion:
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.EA: Extended Application Managing Renewable Resources
Problem 2EA
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Transcribed Image Text:Suppose the population of the world was about 6.2 billion in 2000. Birth rates around that time ranged from 35 to 40 million per year and death rates ranged from 15 to 20 million per year. Let's
assume that the carrying capacity for world population is 20 billion.
(a) Write the logistic differential equation for these data. (Because the initial population is small compared to the carrying capacity, you can take k to be an estimate of the initial relative growth
rate. Calculate k using the maximum birth rate and maximum death rate. Let t = 0 correspond to the year 2000.)
dP
dt
=
(b) Use the logistic model to estimate the world population (in billions) in the year 2010. (Round your answer to the nearest hundredth.)
billion.
OUR TEACHER
Compare this result with the actual population of 6.9 billion.
This result ---Select---
the actual population of 6.9 billion.
(c) Use the logistic model to predict the world population (in billions) in the years 2100 and 2500. (Round your answers to the nearest hundredth.)
2100
billion
billion.
2500
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