The population of the world was about 5.3 billion in 1990. Birth rates in the 1990s 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 100 billion. (Assume that the difference in birth and death rates is 20 million/year = 0.02 billion/year.) (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.) (1/265)P(1−P/100), P in billions (b) Use the logistic model to estimate the world population in the year 2000. (Round the answer to two decimal places.) P =___billion (c) Compare with the actual population of 6.1 billion. (Round the answer to one decimal place.) The difference is ___billion. (d) Use the logistic model to predict the world population in the years 2100 and 2500. (Round the answer to two decimal places.) P = billion in the year 2100 P = billion in the year 2500
The population of the world was about 5.3 billion in 1990. Birth rates in the 1990s 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 100 billion. (Assume that the difference in birth and death rates is 20 million/year = 0.02 billion/year.) (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.) (1/265)P(1−P/100), P in billions (b) Use the logistic model to estimate the world population in the year 2000. (Round the answer to two decimal places.) P =___billion (c) Compare with the actual population of 6.1 billion. (Round the answer to one decimal place.) The difference is ___billion. (d) Use the logistic model to predict the world population in the years 2100 and 2500. (Round the answer to two decimal places.) P = billion in the year 2100 P = billion in the year 2500
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
Related questions
Question
The population of the world was about 5.3 billion in 1990. Birth rates in the 1990s 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 100 billion. (Assume that the difference in birth and death rates is 20 million/year = 0.02 billion/year.)
(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.)
(1/265)P(1−P/100), P in billions (b) Use the logistic model to estimate the world population in the year 2000. (Round the answer to two decimal places.)
P =___billion
(1/265)P(1−P/100), P in billions (b) Use the logistic model to estimate the world population in the year 2000. (Round the answer to two decimal places.)
P =___billion
(c) Compare with the actual population of 6.1 billion. (Round the answer to one decimal place.)
The difference is ___billion.
The difference is ___billion.
(d) Use the logistic model to predict the world population in the years 2100 and 2500. (Round the answer to two decimal places.)
| P | = | billion in the year 2100 |
| P | = | billion in the year 2500 |
Expert Solution
Step by step
Solved in 9 steps with 8 images
Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage