The population of a community is known to increase at a rate proportional to the number of people present at time t. If the initial population Po has doubled in 5 years, determine how long will it take to triple? To quadruple? Solve the above population problem as follows: a) construct a linear first-order Differential Equation (DE) that models the behaviour of the population growth with initial condition; b) solve the DE and find the constant k using the fact that the population doubles in 5 years; c) using the answer in (b), find the value of t, when the population triples; d) using the answer in (b), find the value of t, when the population quadruples;
The population of a community is known to increase at a rate proportional to the number of people present at time t. If the initial population Po has doubled in 5 years, determine how long will it take to triple? To quadruple? Solve the above population problem as follows: a) construct a linear first-order Differential Equation (DE) that models the behaviour of the population growth with initial condition; b) solve the DE and find the constant k using the fact that the population doubles in 5 years; c) using the answer in (b), find the value of t, when the population triples; d) using the answer in (b), find the value of t, when the population quadruples;
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:The population of a community is known to increase at a rate proportional to the number of people
present at time t. If the initial population Po has doubled in 5 years, determine how long will it take
to triple? To quadruple?
Solve the above population problem as follows:
a) construct a linear first-order Differential Equation (DE) that models the behaviour of the
population growth with initial condition;
b) solve the DE and find the constant k using the fact that the population doubles in 5 years;
c) using the answer in (b), find the value of t, when the population triples;
d) using the answer in (b), find the value of t, when the population quadruples;
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
